My info was from a few years back, and they've loosened the requirements somewhat since then.

Anyway, long story short, that means, when we look at all the FBS teams there are exactly two that are P5 without being Tier 1 - Wake Forest and TCU.

There are, however, now quite a few Tier 1 schools that are G5 - UAB, UCF, Cinci, Buffalo, UConn, Georgia State, Colorado State, UTEP, Rice, probably some others. The point remains that being a Tier 1 research institution is a de facto prerequisite to being in a Power 5 conference. Maybe it shouldn't be, but it is. Maybe that ranking fails to take into account how awesome BYU is, but that's the ranking.