I agree that the admissions process is opaque both at Stanford and at other highly selective private schools. Partly because it’s hard to be clear about criteria when the admit rates are so low, and in my view partly because schools do not want to publicize the advantages that those in priority groups get, whether that’s children of prominent alums/big donors, athletes, URMs or some other priority group.
All of this was a lot easier when these schools were admitting 20% or more of applicants, as Stanford and its peer schools were doing 20 years ago.
There is more transparency at some state schools, such as the UC campuses which publish admit rates by SAT, ACT, GPA etc. For that matter anyone can look up what a particular professor is paid at Berkeley. At highly selective private schools, not so much.