Yemenis in the city of Sanaa awoke on Tuesday morning to the sound of rattling windows and a constant buzzing in the sky. It was a noise that brought one word to the minds of those who heard it – "drone" – and a sense of apprehension as they awaited the explosion on the ground that seemed sure to come at any moment.

Citizens of Yemen's capital are not accustomed to drones – strikes usually happen in more remote parts of the country – but the white object circling overhead, harmlessly as it turned out, gave them a small taste of what it's like to be on the receiving end.

"If this is how much fear, terror, and anger what just sounds to be a drone makes in Yemen's capital, imagine what it does in areas it actually bombs," activist Farea al-Muslimi tweeted.

In fact, it wasn't a drone on this occasion. The object in the sky was soon identified from photographs as a manned P-3 surveillance aircraft (or, as Yemeni journalist Shuaib Amosawa dubbed it, a "subservience plane"). Interestingly, the P-3 is mostly used for detecting submarines but has also seen service in Afghanistan where submarines are as rare as they are in Yemen. But what, exactly, was it doing over Sanaa?

Whether or not the plane gleaned any useful intelligence, there is little doubt that the buzzing of the capital, together with the closure of embassies, the sudden evacuation of foreigners and the latest reported drone attack in Shabwa, are as much about psychological warfare as they are about conventional anti-terrorism operations.

Some of the psychology is obvious. The message to al-Qaida's militants is that their plans have been rumbled and they are being watched. If that makes them lie low for a while, the US will claim that its ploy has worked – though the public may never know for sure how serious the threat was in the first place.

But two other messages from this spectacle are more troubling. One is what it says to Yemenis, and the other is what it says to Americans.

The killing of the US ambassador in Libya last September caused political problems for Obama at home, so the desire to protect embassies and their staff now is understandable. Domestically, he has little to lose by over-reacting to the current threat. Even if some terrorism experts dismiss the theatrics as "crazy pants" stuff, it can be expected to play well in the American media, as well as confounding Obama's Republican critics.

The trouble, though, is that this also reinforces American perceptions that Yemen is about al-Qaida and very little else. Viewed from Washington, Yemen is not a real place where people are demanding social justice and democracy so much as a theatre of operations in Saudi Arabia's backyard, veteran Yemen-watcher Sheila Carapico told a conference in January.

In fact, she added, the US doesn't really have a policy on Yemen. What it has instead is a longstanding commitment to the security and stability of Saudi Arabia and the GCC states (Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and United Arab Emirates), coupled with an anti-terrorism policy in which Yemen is treated as an extension of the Afghan/Pakistani theatre. The result, she said, is "pretty much the antithesis" of what Yemenis were aspiring to when they set about overthrowing President Saleh in 2011.

Among ordinary Yemenis, meanwhile, the latest al-Qaida drama has been greeted with scepticism and even some derision. Al-Qaida is often viewed as an American obsession while millions of Yemenis have more basic things to worry about – like obtaining their next meal. They also point out that more people die on Yemen's treacherous mountain roads, or in fights over scarce water resources, than at the hands of al-Qaida.

There is now widespread recognition that drone strikes in Yemen have been counter-productive. Whatever benefits they brought in terms of killing militants who posed a serious threat have been cancelled out by the killing of others who posed no threat at all, and the anger this has aroused among the population at large.

Some of that resentment is now being directed against President Hadi, who was installed by the Gulf states (with western blessing) as Saleh's successor – and it hasn't escaped Yemenis' notice that Hadi met Obama in Washington last week, just a few days before the al-Qaida alert. Obama, as might be expected, was full of praise for him.

Before becoming president, Hadi had no real power base in Yemen and without strong international backing – especially from the US – he would be unlikely to survive for long. That leaves him in no position to resist American demands and at the same time it further damages his support at home. In effect, the US is propping him up with one hand and dragging him down with the other.