affiliated schools do not. It's not too hard to get a non-catholic to attend ND, for instance. It is significantly harder to get a non-member to attend BYU. BYU's pool of recruit-able athletes is just smaller. I like that the new coaching staff is going after these players, but they have little to show thus far. So it means awhile lot more when a really good athlete who is able and worthy to come to BYU big-times the program.
It also hurts that other schools pitch the "BYU-experience" at their school (See Yewtah and Stanford). The more members and coaches they have on their teams, the easier it is to make this pitch. So if the top LDS athletes are going to another school, that impacts recruiting for future years as these athletes have good experiences away from BYU.
So yeah, I don't like it when a good LDS athlete chooses another school over BYU. I don't hate the kid and generally wish him/her the best in the future, but I am admittedly disappointed.