The theory of MAD prevented one side from launching a nuclear war, and this is almost universally known. But was it ever discussed, by say Kennedy and Krushchev, and confirmed? Or was it more taboo and not necessarily discussed by opposing leaders, and simply known by everyone?
It's not the "theory of MAD," it's the theory of deterrence. MAD is one variation of deterrence and it was at times discussed briefly but largely has not been the main way of talking about deterrence. For example, under Eisenhower the official policy was known as "Massive Retaliation," in which the USA would nuke the heck out of the USSR and its allies (!) if the USSR provoked a conventional or atomic war with the USA. The USA had a much larger arsenal, there was nothing "mutual" about it. The language of "assured destruction" started up only in the 1960s, with the Kennedy administration, and was explicitly outlined by his Secretary of Defense, Robert McNamara. By the 1970s this was no longer the formal doctrine of the USA, though the term MAD was applied to it by critics.
In the US case, strategic doctrine of this sort was definitely discussed publicly by people at high levels of government, and Congress was frequently publicly briefed on it. There were broad policy questions about what kind of strategy the US should take to keep deterrence "credible," and especially in the 1960s, public discussion about variations on targeting, e.g., "no cities" or "counter-force."
Soviet doctrine was interpreted largely by people parsing articles that Soviet military figures wrote in un-secret publications (under the idea that they would not be allowed to publish them if they weren't at least partially sanctioned). And sometimes Party leaders made explicit discussions of nuclear matters in speeches and addresses.
There were also doctrines of tactical nuclear war (which are not MAD), and other approaches to the bomb which do not concede or require "total destruction" on both sides. Deterrence is a rather complex and subtle concept, but the essence of it is threatening something valued on the "other" side to encourage or discourage a type of behavior in the enemy. It does not need, nor require, total destruction to function. It does not even require nukes in many cases — there are other ways to threaten something valued in a credible way.
If you are interested in the twists and turns of US doctrine, and its discussion in the public sphere, Lawrence Freedman's The Evolution of Nuclear Strategy is the standard reference.