And the theory will only be conclusively disproven if someone pushes the button.
I don't think two nuclear armed powers have ever declared war on each other - despite two nuclear armed powers currently being in active conflict (India and China) and another few being incredibly geopolitically unfriendly (India/Pakistan and Israel/Iran).
The whole idea behind MAD initially was that if Russia decided to get ideas in Europe, the Western powers would stop them with a nuclear curtain. That's why France has a "warning shot" nuclear doctrine, and the US hasn't ruled out Nuclear First Strike.
IMO, for what it was trying to stop, it worked. Ask people in China and India - it seems to be working for them as well.
EDIT: as an amendment to this: would Russia have been so bold as to invade Ukraine if the 1994 surrender of Ukraine's nuclear arsenal hadn't happened?
It’s kinda like economics. We can’t really prove anything in economics works the way we think it does, but we have a bunch of REALLY GOOD suggestions to support our hypotheses.
MAD isn’t a natural law - it’s a social construct, very much like economics.