Not true.
Play around with https://myintuition.org with a 200K income for married parents and only one child. Many scenarios result in aid, and a lot of it.
I did it for Amherst, Harvard and Wellesley with $200k income, only one kid, $100k retirement, $10k cash in the bank, renting a home and got $35k-ish net costs. I’m sure more savings affects things, home equity for some schools and so on, but this is the sort of scenario we see on CC occasionally where the family income has only recently gotten that high and there hasn’t been a lot of time to save. Those families DO get help - if their kids can get into those schools.
That’s the biggest caveat, I think. Admission. More than one kid is one of many variables that affects aid.
I think OP’s post title was completely appropriate.