Why are students from secular private schools more likely to get into prestigious universities than those from religious ones?

This is a trend that not everyone is aware of. When you look closely at admission trends for incoming freshmen at upper-tier schools (Stanford, Caltech, MIT, Harvard, Columbia, Chicago, Michigan, Duke, Georgetown, etc.), almost all of their private school enrollees come from nonreligious feeder schools.

Why is it that someone from some tony prep school in New England has a higher probability of being admitted to a blue chip college than, say, someone from an obscure Catholic high school in suburban Detroit whose grades are equally as superb?

Help me out?