It means to hit the median family income at those universities you have to come from the top edge of the middle class at least, that is true. That's not very surprising given we're talking about the median at very highly ranked schools. It's moving the goal posts quite a bit given the difference vs the elite rich having to buy their way in due to scarcity.

If you want to dramatically improve your odds of family success in the US, you want to roughly be in the top half of the middle class bracket or above. At least based on school access.

A lot of the top 50 universities do as well or better at accepting bottom 20% income bracket students, as second tier schools do. For reference, share of students coming from the bottom 20% income bracket (ie poor):

UCLA 8.3%; UC Berkely 7.3%; MIT 6.2%; NYU 6.1%; Florida 6%; Chicago 5.5%; Columbia 5.1%; Rice 4.9%; USC 4.9%; Harvard 4.5%; Boston U 4.2%; Brown 4.1%; Stanford 4%; Carnegie Mellon 4%; Duke 3.9%; Tulane 3.9%; Northwestern 3.7%; Michigan 3.6%

Lower ranked schools (but still top ~15%):

Rutgers 6.8%; Illinois 6.1%; Texas 6%; UMass 5.8%; Florida St 5.3%; Michigan St 5%; Oklahoma 5%; Ohio St 5%; Oregon 4.7%; Georgia Tech 4.6%; Oklahoma St 4.4%; Oregon St 4.3%; NC State 4.3%; Texas Tech 4.1%; Washington St 4%; Arkanas 4%; Texas A&M 4%; Alabama 4%; Pitt 3.7%; Minnesota 3.5%; Kansas 3.2%; Kansas St 3.2%; Iowa St 3.2%; Illinois St 3%; Auburn 2.6%; Virginia Tech 2.3%

As a percentage, Chicago takes as many poor students as Oregon St; MIT takes more than NC State; Harvard takes as many as George Tech; Stanford takes more than Kansas St. And so on.

The schools that rank badly on high median family income and low access for poor students are who you'd expect: Princeton, Yale, Vanderbilt, etc. Notre Dame is a particular standout for being terrible, with a median income at $191,000 and only taking 1.6% from the bottom 20% income bracket.