It isn't Hollywood. It isn't an action movie with Sylvester Stallone or Bruce Willis crashing through an upstairs window, spraying bullets. On the contrary, it seems likely that Spielberg or Scorsese would make a more coherent version of last weekend's operation in Abbottabad, appreciating both its moral dimension and the need to get the story straight in advance.

For most of last week, the United States government seemed to be operating from a series of bellicose scripts. US special forces had met fierce resistance in Osama bin Laden's compound; they were involved in a fire-fight lasting up to 40 minutes; the al-Qa'ida leader (or someone) had used one of his wives as a human shield. In Washington, President Barack Obama and his top advisers had witnessed Bin Laden's death, relayed to them live from a camera on the helmet of one of the US Navy Seals. The tension was reflected in a photo taken in the White House situation room, Hillary Clinton nervously covering her mouth.

Now it appears that none of this is true. The US team met little resistance and surprised Bin Laden in a doorway. Yesterday's spin, that he turned to go back into the room, possibly to retrieve a weapon, raises even more questions about why he wasn't captured alive. Distastefully, he appears to have been shot in front of his 12-year-old daughter, while his wife was wounded in the leg trying to protect him. Obama and his aides didn't see the raid live. It isn't clear what they were watching – a DVD of Saving Private Ryan?

Even a halfway-competent script editor would return this dog's breakfast with acerbic comments. But the White House's lamentable handling of the raid has begun to tarnish the celebrations that erupted (tastelessly, in my view) on the streets of America after the killing was announced. Too many people have died to characterise this sombre event as some kind of edge-of-seat sports fixture.

Last year, the President shocked liberal commentators with the announcement that he had approved the "targeted killing" of a US citizen, the Islamist cleric Anwar al-Awlaki, who is believed to be in Yemen. Last weekend's operation shows that the administration has gone further and is operating a policy of extra-judicial execution against its most high-profile enemies, even when they are not actively engaged in terrorist attacks. And that should trouble all of us who believe in the rule of law.

I loathe Bin Laden. I despise his cruelty, puritanism, misogyny and romanticising of violent death. For all these reasons, I'd rather see him demystified in a courtroom day after day than transformed into a martyr. The Allies managed to put leading Nazis on trial at the end of the Second World War, even though they posed a much greater threat to Europe than Bin Laden's pipe dream of a return of the caliphate.

The election of Barack Obama was supposed to mark a definitive break with the cowboy lawlessness of the Bush administration. It was supposed to be the moment when liberals could feel solidarity with the US again, instead of wincing each time an American president claims leadership of the free world. Countries that aspire to a model of universal rights can claim moral superiority over the miserable theology of al-Qa'ida, but there are no exceptions. No matter how great the temptation, and identifying Bin Laden's hiding place falls into that category, democratic leaders have to behave better all the time.

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