When it comes to reporting the conflict in Yemen, Fox News is exceptionally bad. Fox has been fooling its viewers for years but now, with Donald Trump installed in the White House, the problem is becoming a more serious. Trump is a devotee of Fox News: it tells him what he wants to hear – about Iranian influence in Yemen, among other things – and he seems to trust it more than he trusts America's intelligence agencies.

To make matters worse, though, Trump appears to be watching Fox News without giving it his full attention, presumably because he also has his Twitter feed and presidential business to attend to. As we saw from his reference to an "incident" in Sweden last week – an imaginary event which he claimed to have heard about on Fox News – he has a tendency to pick up garbled versions of what Fox actually broadcasts.

There was a similar Fox-inspired "incident" earlier this month involving Iran or, to be more accurate, not involving Iran. On 2 February, White House spokesman Sean Spicer wrongly asserted that Iran had attacked an American warship. Spicer told reporters "Iran's additional hostile action that it took against our Navy vessel" (along with a recent Iranian missile test) was one of the reasons why the US was putting Iran "on notice".

The "American" warship in question was actually Saudi. It had been attacked in the Red Sea at the end of January by Houthi fighters from Yemen who – as Fox constantly reminds its viewers – are "Iranian-backed". The mistaken idea that the ship was American appears to have come from a Fox News report claiming the attack might have been "meant for an American warship".

There was no credible evidence to support this claim but Fox was happy to report it on the basis of quotes from anonymous Pentagon officials even though the Houthis had been claiming all along that the ship was Saudi and identified it – correctly – as a frigate named al-Madinah which had been taking part in a naval blockade along the Houthi-controlled portion of Yemen's coastline. Nevertheless, suggesting that the intended target was American helped to raise fears about Iran and allowed Fox's presenter to tell viewers it "could have ominous implications for the US military".

Fox is always ready to sound alarm bells about Iran on the slenderest of pretexts. Last October, for instance, it got excited about the supposed threat to the US Navy posed by a single 48-year-old Iranian frigate and its supply ship which sailed harmlessly past Yemen to southern Africa, as Iran had said it would do.

While Obama was president propaganda of this kind didn't have much influence on American policy but it now has a receptive audience in the White House. The danger is that if Trump becomes mired in domestic political conflicts, as seems very likely, he may view confrontation with Iran as a way of rallying Americans around him.

Fox, of course, isn't the only source of the scaremongering but it is one of the more extreme examples. In large sections of the media Iran's deep involvement in Yemen is taken for granted: it is assumed to be so obvious that there is no need to consider or even provide any evidence. This is reminiscent of the run-up to the 2003 war in Iraq when it became almost heretical to question whether Saddam Hussein really had weapons of mass destruction.

This isn't to suggest that Iran has no role in Yemen at all but it's important not to exaggerate. The Houthis certainly have some religious affinity with Iran and nobody – least of all, the Iranians – would deny that Iran has given them encouragement. But while describing the Houthis as "Iranian-backed" is factually correct it's liable to be be misleading unless qualified with further explanation. And while it suits Saudi Arabia's purposes to characterise the Yemen conflict as a proxy war with Iran, local factors inside Yemen are actually far more relevant.

There is a very noticeable contrast between the sort of Yemen coverage provided by Fox News and discussions among people who follow Yemen closely for professional or academic reasons and have no particular axe to grind. I have attended plenty of discussions of the latter kind since the conflict began and the Iranian angle is rarely given much significance. On one occasion it was 40 minutes before anyone even uttered the word "Iran".

One possible explanation for this is that the country with the longest, most extensive and most negative history of interference in Yemeni affairs is not Iran but Saudi Arabia. Its meddling over the years far outstrips anything done by Iran.

As for what Iran is actually doing to support the Houthis, available evidence suggests it's not very much – though this may be due more to the practical difficulties involved than a lack of inclination. A key question here is whether, or to what extent, Iran might be arming the Houthis (and supporters of ex-President Saleh who are allied with them).

A recent UN report by a panel of experts looked at this in detail and concluded that if Iran is providing weapons it is unlikely to be doing so on a large scale. The report said:

"The panel has not seen sufficient evidence to confirm any direct large-scale supply of arms from the government of the Islamic Republic of Iran, although there are indicators that anti-tank guided weapons being supplied to the Houthi or Saleh forces are of Iranian manufacture."

One factor here is that the Houthi-Saleh forces may not have had much need (so far) to import weapons from abroad because they already have access to a large part of Yemen's national stockpile. The report noted:

"The data indicate that the legitimate [Saudi-backed] government has potentially lost control of more than 68 per cent of the national stockpile during the conflict. The panel has been unable to determine the size of the national stockpile before the current hostilities, and thus it is not yet possible to realistically estimate for how long the weapons and ammunition will sustain Houthi or Saleh forces in combat until they need major external resupply."

On the question of external supplies, the report considered various ways arms might be smuggled into Yemen from Iran. It discounted the possibility of delivery by air (since the Saudi coalition controls the skies) and identified three possible maritime supply routes. However, these are fraught with difficulties and are probably only suitable for small-scale arms trafficking, as the report explained:

1. Coastal dhows to Houthi-Saleh-controlled ports on the west coast of Yemen

UN report: "Coastal dhows, if en route to Houthi-Saleh-controlled ports on the west coast of Yemen, even if routed via a transit point in Djibouti or Somalia, must pass from the Gulf of Aden into the Red Sea through the busy Bab al-Mandab strait, which is 28 km wide. This is well patrolled by the Combined Maritime Forces, the United States Navy Fifth Fleet and the Royal Saudi Navy. If sent in very small consignments on coastal dhows, it is probable that some shipments would arrive, but many would inevitably be interdicted by naval patrols. The panel has seen no evidence of any maritime seizures to date on this route, which strongly suggests that it is not being actively exploited."

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2. Coastal dhows to Omani transit ports

UN report: "There are only two small Omani ports to the west of Salalah, Dhofar governorate, with road access to the border with Yemen that would be suitable for the offloading of arms. Ship-to-shore transfers across Omani beaches in Dhofar are also possible. The subsequent requirement for vehicles to then transit through the most likely border crossing point at Sarfayt/Hawf carries a higher risk of interdiction by border guards than if ship-to-shore transfers were made directly across a Yemeni beach. Recent land seizures indicate that this route may be in use for small-scale shipments."

3. Coastal dhows to south-eastern ports or beaches in Yemen

UN report: "The only suitable port for the direct offloading of weapons in south-eastern Yemen would be Nishtun, but this is under the control of government forces, meaning that its use would imply a level of corruption on the part of officials. The alternative to offloading weapons at Yemeni ports is, however, to operate a covert ship-to-shore transfer from coastal dhows or small boats across the known smugglers’ beaches at Ghaydah, Haswayn and Qishn. Recent land seizures indicate that this route is also probably in use for small-scale shipments."

Whether weapons are smuggled across the border from Oman or landed on Yemen's southern coast, the hazards of transporting them overland to the Houthis through hostile territory are considerable. The UN report commented:

"The land routes from the border crossing points with Dhofar, Oman, to the nearest Houthi-controlled territory, or from south-eastern Yemeni ports, pass through more than 600 km of government-controlled territory. The probability of large-scale shipments being able to successively use this route without detection is low, but it is possible. The route is being exploited, as indicated by recent seizures by the government. These were all from large trucks and either hidden under other cargo, for example chicken boxes, or were in false compartments of the trailer units ...

"Although anti-tank guided weapons are now being smuggled on the land routes, the panel assesses it as unlikely that the network using these routes could covertly transfer any significant quantities of larger-calibre weapon systems, such as short-range ballistic missiles, into Yemen at the current time. An anti-tank guided weapon is less than 1 m in length and easily hidden in a large truck, while a short-range ballistic missile of 7m in length is much more difficult to conceal."

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Seizures at sea: a question of destination

During 2015 and 2016 there were only four confirmed seizures of weapons in the Arabian Sea and the Gulf of Aden. All four vessels had sailed from Iran but there's no real evidence that Yemen was their destination. The UN report suggests they are more likely to have been heading for Somalia:

24 September 2015: Fishing vessel Nasir intercepted by Australian frigate HMAS Melbourne.

UN report: "The FV Nasir, which departed from Chabahar in the Islamic Republic of Iran, was seized at a position on the most direct and economical track to Hurdiyo, Somalia. This was the destination plotted [and] recovered as evidence by HMAS Melbourne. Mobile and satellite phones were also inspected during the seizure operation and subsequent traffic analysis from data provided by a [UN] member state provided further evidence that the originator was based in the Islamic Republic of Iran and that Somalia was the destination for the shipment ... The master of the FV Nasir was also in contact with known arms dealers with links to a former pirate, Isse Mohamoud Yusuf (“Yullux”), and the leader of the ISIL faction in Somalia, Abdulqadir Mumin."

27 February 2016: Fishing vessel Samer intercepted by Australian frigate HMAS Darwin.

UN report: "The FV Samer was seized at a position 130 nautical miles south-east of the most direct and economical track from Chabahar, Islamic Republic of Iran, to Boosaaso, Somalia, this being the destination port assessed as likely by HMAS Darwin. This position is further away from the Yemeni coast than the most direct and economical track and suggests that a more likely direct destination was the eastern smuggling ports of Somalia than Boosaaso."

20 March 2016: Unknown fishing vessel intercepted by French destroyer FS Provence.

UN report: "The unknown fishing vessel was seized by the FS Provence at a point on the most direct and economical track from Chabahar, Islamic Republic of Iran, to its declared destination of Qandala, Somalia."

28 March 2016: Fishing vessel Adris intercepted by American patrol ship USS Sirocco.

The interception by USS Sirocco was announced in a press release by the American Fifth Fleet and reported in the media but despite two requests from the UN experts, the US has still not disclosed the location of the seizure or provided evidence to support its claim that the shipment "was likely bound for Houthi insurgents in Yemen".

This is not the only instance where countries engaged in the struggle against arms smuggling have been less than forthcoming with information for the UN panel. Regarding seizures on the overland routes, for example, the report notes:

"The panel has requested detailed information on seizures from Saudi Arabia, the United Arab Emirates and Yemen [i.e. the Hadi government]. Only the United Arab Emirates has responded to date."

Nor have the Saudis been eager to elaborate on reports of a possible fifth seizure of weapons at sea in 2016:

"Media reports claimed that two small dhows had been captured by the coalition led by Saudi Arabia off the coast of Salif, with conflicting reports stating that they had been destroyed by air strikes. Saudi Arabia has not responded to the panel’s requests for more details on the reported incident or incidents."

It does seem a bit odd that governments which readily accuse Iran of arming the Houthis are not more enthusiastic about providing credible evidence. But perhaps they assume the public is already persuaded and needs no more convincing – and they could be right about that.