"What does beating Butler have to do with the schedule being good or not? Butler is Butler whether the Gophs win or lose."
Art, I can't speak for Col Nathan (correct me if I'm wrong Col), but I think his point is the outcome of the Butler game will play a large roll determining whether the overall nonconference schedule gets significantly better.
If the Gophers win and go to the winner's bracket, that pretty much assures 2 more games vs. quality opponents (i.e. UCLA/Clemson/Texas A&M/West Virginia) and a huge SOS bump. If they head to the loser's bracket, their schedule rank (presumably) will take a hit because they're not as likely to play the same quality of opponent and they'll have less opportunities to pick up a quality win(s).
Edit: I see that Col Nathan has already replied.