A school like Miami will not be able to participate in top nonconference tournaments along the same lines as a high major program; however, some of the tournaments that aren't as prominent do have mid- and low-major schools playing. Now, that's not necessarily going to change their strength of schedule a lot, but they could pick and choose one that has a little bit stronger mid-majors.
I don't fault Miami for nonconference tournaments as much as the fact that they didn't play any guarantee games. You're a MAC school, you play guarantee games. That's how it is. The MAC is rated the 17th-best conference per KenPom. MAC programs aren't even mid-majors, they're low-majors. You play high majors on the road when you're a low-major. Mid-majors can get away with not playing the big boys on the road, but even they sometimes choose to do it.
