The scary thing about the Cold War was that the participants generally had the best of intentions (aside from a few people like Curtis LeMay, and they never really got presented with the opportunity to express their evil side) but disaster could have easily happened anyway, purely by accident.
And I really shouldn't put this in the past tense. All of this stuff is still there. We all seem to have just decided to collectively pretend that MAD went away when the USSR dissolved, even though there are still thousands of missiles and nuclear warheads ready to wreck civilization at a moment's notice.