BYU is not an elite school and it never intended to be. It's a church school in Utah.

Here are BYU's admissions stats, from its own site:
https://admissions.byu.edu/entrance-average

2013
Admissions rate: 56.2%
HS GPA: 3.82
ACT: 28.52

http://theivycoach.com/2017-ivy-league-admissions-statistics/

The admission rates for Ivies range from 6% to 15%
http://collegeapps.about.com/od/theact/a/act_side_x_side.htm

The median ACT scores for Ivies is closer to 33 (they show the 25% and 75% score for each school).
https://admission.stanford.edu/basics/selection/profile.html
For Stanford, 57% of their applicants have a 4.0 HS GPA and 72% had an ACT in the 30s.

Forbes ranks it #79 in the US, which puts it in the same class as Texas and Maryland. Utah is ranked 141 on that list.
http://www.forbes.com/colleges/brigham-young-university/
http://www.forbes.com/top-colleges/list/

BYU is a good school and I got a good education at a decent price. I went to two grad schools after BYU and never once felt behind my classmates in undergrad prep. Claiming that it's as good as an Ivy makes you look insecure in your education. As Lisa Simpson said, “Anything that’s the something of the something, isn’t really the anything of anything.”