I really don't follow what you are saying. If the information can be independently verified, then you don't need to torture someone. If it can't then it is no good. The fact is that people who confessed to being witches knew that they were dooming themselves to a painful death, and often that their families would lose any wealth that they had built up. They still did it.
A bit of information is either true, or it is false. If it is true and it is useful, then, by definition, it is verifiable. Its very usefulness, e.g. in tracking down a criminal or finding a hidden cache or in decrypting a computer file, is self-verifying. If a bit of information cannot in theory be verified, then there is no conceivable useful purpose to which it could have been put. A prisoner's confession that he is a witch, or, more plausibly, that he believes in God, or that he likes cranberry juice is unverifiable and therefore useless. It's a bit different if he confesses to a crime but claims that he had no accomplices. That is verifiable, but it is similar to proving a negative, so that it requires more work and may in fact be close to useless in practice. If he claims to have accomplices, then those accomplices can be picked up and their stories checked out. That is both verifiable, and, if true, useful.
As to your second paragraph: I don't understand - someone doesn't initially talk, then they start saying anything to get the torture to stop. Also a significant fraction (upthread I think a figure of 20%) of the detainees were innocent and knew nothing.
My point is that if the prisoner knows the truth, then the truth will come out. There may be a lot of false stuff too, but (truth plus falsehood) >= nothing and is strictly greater than nothing in most cases. The idea that eliciting falsehoods is somehow a huge negative is nonsense. The interrogators always have the option of expending zero resources on any of the information that comes out.
Also, if falsehoods were such a waste of resources, then presumably an enemy prisoner would be trying to utter falsehoods anyway. It's not so easy to tell lies in a consistent way, though. Especially when you don't know what information the interrogators already have.
We also have the case of at least one Al Quaeda prisoner who had been cooperating with an FBI interrogator and who after being taken by the CIA, became "unresponsive". That was an own goal on all levels.
Yes, well, that would be a disastrous result. However, the FBI and CIA are rivals, and they hate each other, so I'd treat such claims by FBI interrogators with a good deal of skepticism.