That is really what it comes down to. They were looking for one school, Utah fit the bill better than BYU did. If you remember the climate at the time, Prop 8 had just happened and public opinion of the church was pretty low. It wouldn't have been the best PR move for the most liberal of the football conferences to admit BYU at that point in time (everyone thought we hated gay people). The "research school" excuse was just to cover this without actually having to state it.
It should be said that if the roles had been switched, Utah football would be in a significantly worse position than we are now.