But the contradiction is in the mathematical model not reality. Even a totally random universe follows some kind of distribution, which can then be modelled (which is exactly what QM is).
He's assuming a mathematical model that faithfully represents reality, hence "reality can't contain contradictions". We're not going to one day find a contradiction and vanish in a puff of logic, the ultimate model of reality will be contradiction-free.
So then you're saying reality can't have a logical contradiction? Seems like you're agreeing with the original statement.
>Even a totally random universe follows some kind of distribution
Which is just a kind of rule.