Welp, you have a point. I mean one side can have 2,000 warheads and the other side can convince everyone that it has 2,000 warheads, even if it doesn't. In that case, the side with the actual warheads is convinced of MAD and doesn't attack. That is.......unless the side that is faking does such a good job of it, that the side with nukes vaporizes them while believing they are under attack.
I'm fairly confident that MAD kept the US and USSR at a standoff for half a century.
Launching nukes is a complicated bureaucratic process where the entire chain of command from political to military has to commit to the mission.
How can you know that the chain of command of one country committing to the launch would imply a perfectly mirrored commitment from the chain of command of another country?
Protip: you can't know that. Because this issue relates to depths of human psychology that haven't been explored, ever in history. Experts in the field still today have no idea whether proliferation would contribute to greater peace or lesser peace, but they opt for letting "sleeping dogs lie" by sticking to anti-proliferation as the
seemingly safer option. All history (of the cold war) has proved so far, is that the issue of nukes has a weird effect on human psyche, creating unpredictable gaps in the command chain. Where half of the officers may commit, but meet opposition from the other half. So you can only make far-fetched assumptions. (and I'm not even mentioning the effect of proliferation on the nature of military and political bureaucracies)
Assuming mutually-assured destruction is as plausible, as assuming one country launching a strike and the other refusing to retaliate. Until today, all nuclear actors opted for letting "sleeping dogs lie", however, regardless of the history of the cold war, they didn't actually stop pursuing "first strike" capability, which only signifies that MAD as a theory is quite contested even within the political elites of nuclear powerhouses.
Opting for a seemingly safer option out of a fear of the unknown doesn't imply "proof" of anything.