This is an older article (2012) showing how one excellent UK university does admissions. I think it covers some of the challenges your statement implies and showing some of the hard work such universities do. There's an interesting anecdote about a student who tutors believe simply won't keep up with the course due to starting from too far back (they are described as being from a hopeless school), another where a student has been guided by their school to study the wrong classes. In the UK, education is split into 'state schools' (free) and 'private schools' (paid for), and within both bands there is much variety, but in general private schools have better outcomes (as do state schools in wealthier areas). In the UK, this 'private vs state' debate is one of the most polarizing - should you be able to pay to win? At least at Cambridge, careful effort has dramatically changed representation over the last 20 years - from approximately 50% in 2000, to 62% in 2012, to 73% now (with private schools representing approximately 15% of students at age 18 this is a pretty good effort), and I think this article represents some of the hard work that has to go in to ensuring equality of opportunity (they describe: careful thought of each application, metadata held about schools, analysis of school provided documentation, etc, review, second chances, etc. they also do a _tonne_ of access things specifically designed to widen the funnel at all parts of the pipe).
I don't know or think it's the same for Stanford - after all, 16% of Stanford admissions are legacies - but it can be done with hard work! I'd certainly be interested in a similar article for Stanford, though.
https://www.theguardian.com/education/2012/jan/10/how-cambri...