I'm also from Boise, grew up a fan, and still have many family members there who are huge fans. I was offered a football scholarship by them the year after they won the 1-AA (precursor to FCS) national championship, and turned it down to pay my own way at BYU.
When you say "For most of the time, BYU didn't win enough to be considered a rival, anyways," it really shows your age and recency bias. The fact that BSU would DARE "look down" on BYU is hilarious. BSU is a cute, quirky, smurf-turf little program who found success against inferior competition, won a couple of high-profile games, and took advantage of BYU a few times when they were at their best and we were at our worst. They will ALWAYS be a little brother and the reason so many BYU fans don't like them is because so many of their fans laughably think otherwise. As a school and a PROGRAM, there is just no comparison.