Why do we buy that Bush Administration torture is intended to extract the truth?

We read now about an Al Qaeda prisoner whom we sent to Egypt to be tortured. He eventually came up with a fabricated story that Saddam Hussein had trained Al Qaeda members in chemical and germ warfare. This testimony became a favorite piece of smoking-gun evidence, cited repeatedly by top officials in favor of their war. He has since recanted.
It is gross naivete to say “You have defeated your own purposes. You wanted to get the truth, but testimony under torture is notoriously unreliable, so you ended up getting falsehoods instead.”
But what about when it was falsehoods you were seeking in the first place? Torture is routinely used to extract confessions from the innocent, force them to implicate innocent associates, and to substantiate insidious Big-Lie policies.
We know the falsehood that got this man out of Egypt. And we know that the truth led only to continued torture.
Stalin’s infamous “Purge Trials” showed the world a series of pitiful, torture-broken defendants incriminating themselves and others, and detailing elaborate fantasies of conspiracy against the state. Do we say that Stalin’s inquisitors had defeated their own purpose, because they didn’t get the truth?