Isn't this exactly the moment where he is wrong? Even if all three of these would happen simultaneously, it would still be easier to ensure human continuity on earth, not on mars. A mars colony would have to be underground to escape the radiation and poisonous atmosphere - but of course you could also build an underground shelter on earth. And have better gravity, easier energy sources, endless amounts of water and so on for free.

A mars outpost after a nuke party on earth would simply die, as it is completely unfeasable to both a) develop it so far that it becomes self-sufficient and b) not become a military target along the way simply because of its size.