Maybe you've only spent time around PhD candidates at Ivy League schools where people are more likely to have access to wealth, but if you've spent any time at all around PhD candidates you'll find this is generally not the case. As a PhD candidate from a lower SE class, I've found that the majority of my peers are from a similar class. However, I am not connected to a private university though I am in medicine.
Studies on this show great variation across doctoral fields. Economics doctoral students tend to come from more affluent backgrounds, while the majority of Social Sciences doctoral students are from a lower SE class. Overall there seems to be a trend that doctoral students in fields with more lucrative career prospects tend to come from a higher SE class.
From what I have read, your claim only applies to the majority of faculty members, which tend to come from backgrounds with an income that is higher than the national median income.