I knew a prospective student with above a 3.8 unadjusted GPA, 28 ACT, terrific 2-sport athlete (as in one of the very best statewide in one sport and college-scholarship material in the other) musically inclined and everything you'd want in a BYU student. Came from a highly-LDS populated area.
Did not get accepted as a freshman. I believe the lack of a Calculus class may have been the deciding factor. Despite a competitive ACT, the academic rigor may not have quite been there. I can't think of anything else.
This student accepted an athletic scholarship to a reputable, smaller school and excelled there academically, which included acing Calculus.
We've had tremendous young men and women from our heavily-LDS community not get accepted. However, when peeling back the onion, ACT score and or lacking higher math are typically the culprits.
There have also been a lot of kids get in with credentials far below the dude's daughter in the OP--like several from our ward alone. It's very tough, and there are some head-scratchers about who does/doesn't get accepted, but we've found it's not the nightmare that some around here make it out to be either.