We aren't talking about making a million dollar donation to get your son into school. That happens, sure, but it's an extreme example.
Here are things that richer people can do easily & poorer people struggle with.
* Not working or working part time for four or more years
* Moving across the country
* Living in places with high cost of living (think Stanford, Berkely, NYU)
* Getting tutoring for the SAT, taking the SAT multiple times
* Going to a high school where the teachers give a shit
* Having people in your life who went to college & can help you apply
* Having extracurricular activities that show you'd contribute to campus life
* Already being comfortable with being interviewed at age 18
These are just what I could think of in a few minutes. Scholarships _do not_ level the playing field (though they certainly help).