And it doesn't change my point. They're not going to give BYU an auto-bid to that game. Also, the "group of five" representative is not locked-in to the Cotton Bowl either. The highest-ranked champion from the "group of five" conference is guaranteed a bid in one of those major bowl games, but the selection committee can place them in either the Fiesta Bowl, Cotton Bowl, or Peach Bowl (whichever is the best matchup or geographic fit).
Also, even if the Cotton Bowl COULD contract to take BYU, why would they do it? It makes absolutely ZERO business sense to do so. They only way they'd even want BYU in their game would be if they're undefeated and ranked in the top 10 - and if that happens there's a good chance that they'd still end up there anyways as the at-large.