Given the alternatives presented in the OP's post, I would certainly strip UNC of their titles. For decades, the run-of-the-mill college basketball fan has thought that UNC was this squeaky-clean, preeminent basketball program representing this preeminent bastion of higher learning, when, in reality, the emperor had no clothes. Those pretenders must be un-masked.
By contrast, as far as I know, the run-of-the-mill college basketball fan has never thought that U of L was anything more than what it has been shown to be - a classless outfit that manages to hook in some good players from to time, by any means necessary, to be coached by a guy who - while an utterly despicable human being - is a very good basketball coach.