You’re wrong. And I don’t know what people from other states you talk to, but here is the reality: non LDS people only know BYU as a Utah school. They’ve never heard of a BYU school in Idaho or Hawaii.
LDS kids know the difference. I don’t know any kids who got accepted to BYU but not BYU Idaho. But I know dozens of kids who got rejected from BYU and went to BYU Idaho as a consolation prize.
The academic standard at BYU Idaho is improving, but let’s not pretend it’s the same.