I remember reading a few cases of torture where the detainees where forced to sign false confessions.
There is the case of the the Tipton Three, British Muslims, who the US said were in Afghanistan with Al Qaeda in 2000. The problem with that is, their passports, travel records, employers, all show that they didn't leave the UK in 2000. MI5 actually backs up their story.
Another example is the case of Ibn al-Shaykh al-Libi. He was tortured by the Egyptians (one of the CIA's favourite places to 'outsource' torture).
He signed documents that were used the sole source to "prove" a link between Iraq and Al Qaeda. This was then used in a speech by Bush in 2002 to persuade Congress to get behind the invasion of Iraq, then just a few months away. Powell also repeated the same garbage at the UN.
He later said, it was false, and he signed it so they would stop torturing him.
He claimed that his interrogators staged a mock burial, locking him in a box for 17 hours, and after they let him back up, they punched and beat him until he agreed to sign the detailed confession.
The only people who benefited from this torture, were the ones who wanted a convincing argument to attack Iraq, and didn't care that the argument was a work of fiction.
Torture
is terrorism. It's politically motivated and has nothing to do with saving lives.