I think that this particular fact adds to the paradox.
For better or worse, due to being a church owned school BYU fans and athletes are held to a higher standard. In many ways this is true for ANY school that is owned/run by ANY church or organization that has an identified "honor code" type set of rules.
It is irritating when Y fans and athletes themselves say "look at us, we have better morals/standards/values/etc."
It is equally irritating when anyone else points fingers and says "look at you, you did ___ and you are supposed to have 'better' morals/standards/values/etc."
On the other hand, BYU certainly doesn't have a corner on being an organization that wants to be known for doing things their way - and be known for their way standing for something better than the norm. How many other places have made comments along the lines of "We don't do that. We are ____", or "We're better than acting that way, we're _____".
I've certainly heard that from everyone from little league to high school - and that's just referring to sports teams.
I don't think this will ever change. BYU will always have certain church-related standards. There will always be self-righteous people who use those standards to lift themselves above others. There will also always be judgemental people who use those standards to should "hypocrite" everytime someone slips. It just is what it is.