I've attended every Utah v BYU football game at both RES and LES over the last 18 years. Do you hear more swear words at RES? Yes. But for the choice of vocabulary, nothing is different from my perspective. I am a Utah fan, so take that into account.
I'm not sure what the "fabricated incident" is you are referring to, but did it involve a fan or BYU as an institution or BYU players? Also, did the fabricated incident have a racism or religion aspect to it, or was it just run of the mill bad behavior?
If anything, BYU, as a religious institution, takes the high road when they don't have any need or reason to do so. Kudos to BYU for that. But don't expect every secular institution in the country to do the same.