I also went to an elite prep school except it was the 2010s. You're right that the kids there prove themselves. The top ~15% of students there would have found

I also went to an elite prep school except it was the 2010s. You're right that the kids there prove themselves. The top ~15% of students there would have found the top universities under-challenging, except maybe MIT. The top 50% would've been on par. But guess who got into the top private universities from that prep school, not the top students. Most were legacy, donor families, or really crafty liars. So overall I would consider the prep school kids going into top private schools under-qualified (public unis are different), though not exactly because they're from prep school.