The people who seek out and attend institute for four years will have somewhat similar activity rates to those who attend church schools. Institute is a pain in the butt if you already have a busy schedule and a social life so it makes sense that those who still go will remain strong in the faith. What isn't being accounted for are the students who would have applied to a church school but did not attend for whatever reason, then don't attend institute classes and end up going inactive.

Measuring BYU applicant activity rates with BYU attendee activity rates would paint a much clearer picture.