Tuition is free at Stanford if your parents make less than $125K. Everything is free if they make less than $65K. 78% of Stanford students graduate debt-free.
It's really important to understand that the elite non-profit private education system functions differently from mainstream higher ed. Elite private schools are already socialist: they jack up sticker prices for high-income parents and solicit their wealthy alumni for donations so that lower-income students who get in can go free. If you get in, you will probably graduate in fairly decent financial shape, particularly considering that many local companies give good internships to Stanford students.
The folks you hear about with six-figure student debt figures are typically products of mid-tier private colleges. These organizations don't have the endowment or wealthy tuition-payers to be able to subsidize lower-income students the way elite institutions can, and so they just put everybody in debt. Then their graduates get out into the working world and are indistinguishable from any other mid-tier private college graduate, and so they get indistinguishable (i.e. low) wages.
The ones you are talking about are those who earned need based financial aid for scholastic achievements. If that’s what you mean by “elite” I guess you’re right in the sense that it’s difficult to manage and they’ve done so, but that’s a strange way to describe hard working students.