My PoV is that an applicant applying to college without the hooks listed below would have the same results if they attended HM or Riverdale.
A couple of things to consider: The matriculation data includes recruited athletes, legacies, donor’s kids, and at some schools, faculty brats. Those categories tend to be overrepresented at these schools. The unknown is where these parents went to college and/or work.
For the rest, colleges admit applicants, not secondary schools. A top private may allow the student to develop into a stronger applicant, but so can other schools. Choosing a school simply based on matriculation data is folly.