I meant it didn't eliminate all circumstances.

I think you've pointed out a flaw in my argument. The statement "MAD made nuclear war impossible" is demonstrably false - nuclear war could still happen with MAD. The statement "MAD prevented nuclear war" could still be true - nuclear war may have taken place (and probably would have been more likely) in the absence of MAD, and therefore MAD did prevent a nuclear war.

There is empirical evidence against the MAD hypothesis.

During the Cuban Missile Crisis, a Russian submarine believed that nuclear war had broken out. Three officers on board the submarine were authorised to unanimously launch a nuclear torpedo. An argument broke out among the three, in which http://en.wikipedia.org/wiki/Vasili_Arkhipov was against the launch, preventing a nuclear missile from being launched (and presumably a nuclear retaliation would not be unlikely).

Let's assign a probability that one of the officers would be in favour of launching a missile. Given that 2/3 in our sample were in favour of launching the missile, let's assign the probability to be 2/3 for any single officer. Therefore, the chance that a missile would have been launched is (2/3)^3 - 27%. Even if the probability was less than 2/3 (and people's opinions are interdependent - one person could convince another, or one person could take a contrarian stand), nevertheless it still could have happened. And this wasn't the only time that there almost was a nuclear war. (Incidentally I believe these cases show that an individual effort can at certain points have a huge impact - proof of both the butterfly effect or the 'great man theory' - as long as you redefine 'Great Man' to be a person in the right time and place).

As to the question of whether MAD worked - well it can be certainly argued to have helped, but it demonstrably did not prevent circumstances that could lead to a nuclear war.