Claims that the torture of detainees was directly responsible for the intelligence that tracked down Osama bin Laden are fanciful at best and cynically manipulative at worst.

Leave aside for a moment the moral repugnance of torturing people, the thousands of innocents who were detained and mistreated alongside the likes of Khalid Sheikh Mohammed, and the clear evidence that brutal behaviour on this scale is more effective as a recruiting sergeant for extremism than anything else.

Even with these fairly significant exceptions, it is still clear that the line peddled by George W Bush apologists (such as this Republican congressman) – that what this episode teaches us is that waterboarding works – is as wrong-headed as it is naive.

First, no credible link even seems to have been presented between the torture of detainees and the information leading to Bin Laden. In fact, insiders from both the Bush and Barack Obama administrations are saying the opposite.

Donald Rumsfeld himself had this to say on Monday: "It is true that some information that came from normal interrogation approaches at Guantánamo did lead to information that was beneficial in this instance. But it was not harsh treatment and it was not waterboarding."

Meanwhile, asked about whether waterboarding played a role in finding Bin Laden, John Brennan – counter-terrorism adviser to Obama and, it's worth remembering, a key figure in the CIA under Bush – replied: "Not to my knowledge. The information that was collected over the course of nine years or so came from many different sources: human sources, technical sources, as well as sources that detainees provided. It was something as a result of the painstaking work that the analysts did. They pieced it all together that lead us to the compound last year and resulted in the very successful operation [on] Sunday."

While AP carries this information from former intelligence officials: "[Khalid Sheikh] Mohammed did not reveal the names while being subjected to the simulated drowning technique known as waterboarding, former officials said. He identified them many months later under standard interrogation, they said, leaving it once again up for debate as to whether the harsh technique was a valuable tool or an unnecessarily violent tactic."

Second, intelligence-gathering is never a simple case of A to B. The information leading to Bin Laden will have been drawn together from a myriad of sources – among those that have been pointed to so far are phone taps and, according to the White House, "Pakistani co-operation". A former CIA operative quoted by the BBC goes still further: "Intelligence agencies like the CIA and the US military will simply put out disinformation to protect the real sources, which could have been anything from intercepts to the Pakistani government itself."

And third, a key problem with torture is that it produces an impenetrable mix of falsehood as well as truth. People will say anything to make it stop – take, for instance, Ibn al-Sheikh al-Libi, tortured into claiming a link between Saddam Hussein and al-Qaida. Even assuming "good" torture evidence really did lead to Bin Laden, was this really worth the consequences of the "bad" torture evidence weighed in the lives of Iraqi civilians and coalition soldiers?

So does the saga of Bin Laden's death help the case of the pro-torturers? Not really. Even accepting their own best-case scenario – that torture gave them the evidence that helped them trace Bin Laden – it also, in different cases, gave them the clear falsehoods that led to a massively costly war in Iraq based on the misguided belief in links between Saddam Hussein and al-Qaida.

More importantly, no clear link between the mistreatment of detainees and the information leading to Bin Laden has actually been presented – in fact, the comments from Rumsfeld, Brennan and others have pointed to the opposite, as have the White House briefings stressing the huge range of intelligence information involved.

But even if you do decide to take the facile and misleading arguments of certain Bush-era apologists at face value, that Khalid Sheikh Mohammed + waterboarding = Bin Laden, maybe spare a thought for the thousands of others put through this ordeal (and worse) at Guantánamo and CIA black sites around the world.

What happened to it being better that 100 guilty men go free than one innocent man be imprisoned? Here, one guilty man has been killed while hundreds of innocent men have been imprisoned and tortured – that is not justice.