of talking past each other. BYU had three or four prominent incidences within the space of a couple years (the Memphis brawl, the nut punch, the Emery punch....and wasn't there another football incident where a lineman or linebacker rolled someone's ankle with his arms after a play right in front of a camera?). This is perceived by the general public and sports commentators as being much dirtier than a lot of in-game penalties for things like helmet to helmet or other personal fouls.
Note that I'm not saying BYU is actually a dirty team, or any dirtier than Utah - in fact, I think they're just like most other schools when it comes to that, which is to say, no big offender particularly. But you can see why the public perception recently might be a dirty team, even if it's just a few highly spotlighted outliers that stick in people's minds.