The premise that private school gives an admissions boost may be true but it seems to me that this argument would only necessarily be true for the marginal stud

The premise that private school gives an admissions boost may be true but it seems to me that this argument would only necessarily be true for the marginal student, ie public school student A and private school student B both just cleared the bar for admission then student A had to rely more on their own talent. If I had to guess PG is thinking about Ivy/Stanford where admissions are so strict that almost everyone is near the margin and needs some luck to get in. My university was not competitive and the average student was comfortably over the bar so that no such relationship holds.