That is the fact pattern I was calling out.
FWIW, I had scholarships to both and went to USU pre mission, and BYU post mission. I don't know that I have met anyone who did it the other way around, certainly not anyone who had a full ride to the Y.
My point is not that it never happens, but when I went to USU for that fun first year, I was excited to learn that a lot of people apparently had full ride offers to BYU but just didn't want to go there, and chose USU. In fact it appears more people at USU had full ride offers to the Y than there were scholarships available.
I liked my time at USU and knew some very smart people there. I just thought it was funny how often I met people with full rides to the Y, to the point it just didn't ring terribly true after a while.