The issue with BYU losing the edge in that rivalry is something that predates Bronco's era. There's the 1996 game if you're looking for the last time BYU had an easy win over the Yewts. You'd have go back to 1991 if you're looking a home game where that happened. But since 1996, any victory BYU has had in that rivalry has been the result of some dramatic last minute score or defensive stand or Utah simply missing a field goal.
There are things Bronco could've done differently to better prepare BYU for those games but I don't think Bronco tattooing "Beat Utah" on his right butt cheek would've turned the tide on those games.