I did not see in the data set where the interviewee's family wealth or upbringing were mentioned. Would you mind providing a link?
That doesn't sound like 'tons'.
I worked really hard to be able to get into an elite university and to get the scholarships to pay for it. When people automatically assume that my education means my family is wealthy, it discounts the enormous amount of work which I (and other low-income students) did to get there.
You should state ".. and I had to work my way in there - my folks aren't wealthy!" as a bi-sentence every time you mention your education. I bet most people immediately would understand what it implied: This is an achiever!
Even if fewer poor students get in, that definitely does not mean you can make the reverse assumption: that everyone who attended an elite university is wealthy. For all we know, these results are dominated by poor students who worked hard enough to get into an elite university (which, by the way, wouldn't be a crazy assumption: my CS classes had a lot more income diversity than, for example, political science ones).
The data here is perfectly compatible with a contradictory hypothesis: upbringing does not matter and top schools/employers are good at selecting future high performers.
I'm not endorsing either hypothesis, but the data here supports the above just as much as your hypothesis (which is to say, not much).