There is one flaw with that thought. Only one of those two schools is owned by the church. The parallel you drew doesn't quite work.

It is true that that a missionary doesn't have to like BYU, but to say it in a Provo sacrament meeting is NOT the same as saying something about not liking the U in a SLC sac. mtg. It would be more like a catholic going to a Catholic Church in South Bend, Indiana and saying that he never applied to Notre Dame because he never cared for the Fighting Irish...would be kind of a foolish thing to say. It's okay to feel that way, but shouldn't be shared over a pulpit in certain places. You know?