Stanford (like most top private schools) offers very generous financial aid. Very low tuition for students whose families make < $125k, and very low room and board for students whose families make < $65k. https://news.stanford.edu/2015/03/27/new-admits-finaid-03271...
Of course poor students are less likely to get accepted because of less access to private tutors and other support.
And the rich students who get in because of their rich parents don't have to go through the same rigorous smartness and motivational filters that poor students do.
I'm willing to bet the poor students on financial aid aren't such entitled misogynistic douchebags as the rich ones [1] who go on to found companies that are "only for rich people".
In theory, that is great. In practice, it does little to level the playing field.
Many capable high school students are not even aware that schools like Stanford exist, and cannot even begin to conceive what acceptance into such a radically different world would even mean. I surely didn't. It is also possible that those students who are aware, and do aspire to receive this aid, have family members who actively sabotage their efforts.
My point is that it is possible that no one in the history of their high school, or anyone they have ever known, has attended such a school. The student nor their parent(s) have the mental framework to reason about it.
You are correct. I vaguely recall seeing a study that concluded that rural kids at the top of their class were much less likely than urban kids to go to college and, iirc, a factor was that they were much less likely to know about scholarship opportunities. So, they just did not think it was possible because they did not have the money and never even looked into other options since those other options were essentially unimaginable. They and their entire social network were drastically less likely to think college was a viable option and, so, their education ended at 12th grade.
This is a real problem not only for the rural youth essentially cheated of opportunity, it is also a problem for a nation missing out on untapped talent.
Of course poor students are less likely to get accepted because of less access to private tutors and other support.