I never said BE teams were mid-majors, but in any given year there is a lot of overlap. Using ESPN’s power rankings, here’s the back end of the Big East this year:
BE: 54, 59, 65, 66, 70, 72, 95, 100
Here’s the top of the top four mid-major conferences:
A10: 33, 46, 62, 80
American: 50, 64, 82
Mountain West 29, 53, 56, 69, 74, 75, 87
WCC 9, 41, 39
I’d call that considerable overlap.
Going back a few years, a bit more overlap AND a few teams performing like mid-majors (power rankings going back a few years):
GTown. 70, 86, 194, 216, 177, 71
DePaul. Maybe worse.
SH. 54, 151, 53, 70
Butler. 66, 66, 75, 123, 145, 121
Though I was just joking around, I stand by my statement that there is considerable overlap.