Maybe he signed an NDA where he is not allowed to reveal who their biggest rival is and who they think about the most.
It is almost more respectful to BYU's brand not to bring them up in Ute press conferences directly. Like, maybe he doesn't want to look like he's using BYU's name and brand to boost his own profile.
I have seen this in industry with certain well-known relationships that get alluded to obliquely.
Also, I love that his wife gives him crap about it. What's up with that?