There is a problem inherent in discussions of whether torture or other forms of coerced cooperation work or not. People seldom respond directly to the threat or the coercion but usually take advantage of some sort of intermediary proposal or other face saving option.
The article linked above discusses this problem in the context of KSM. On the one hand, the actual cooperation that KSM offered was to an agent that specialized in building rapport with the prisoners. On the other hand the cooperation only came after he had been water boarded. Was the cooperation the result of the coercion or the torture? It is impossible to say in any single case.
The same problem comes in at the level of states. Libya gave up its nuclear weapons program shortly after the invasion of Iraq, but the negotiations had been going on for some time before the invasion (though not, if I am not mistaken, before the invasion had become a likelihood). It is possible to argue that he would have given them up regardless.
Even the great appeaser, Neville Chamberlain, demanded something in return for his capitulations and appeared to the last that the Fuhrer's signature meant something. He never thought of himself as giving into the threat of force and coercion.
My own view is that the threats and coercion are primary but it is hard to argue any single case convincingly one way to someone who truly believes the opposite.