They'd win the Sun Bowl (which was more exclusive back then) and lost to LSU 6-0 in the Sugar Bowl (a big 4 bowl) and ranked 6. They manhandled WAC competition, including ASU and UA, and especially BYU.
That all fell apart with the Black 14. Of course that wasn't BYU's fault, but there is guilt by association in their little minds.
I lived in Laramie back then. There was also an anti-Mormon undertone, which seemed strange with otherwise very friendly people.