Is this why private universities look more appealing than public universities?

Yet fpr example U Mass Amherst has a higher percentage than MIT, when they are located in the same area. Some are based in regional differences, the university of Montana is going to be cheaper because salaries across the board are cheaper (and not being an accountant, I don’t know how F and A charges work, does that include not just administrative costs of the grant, but does that include things like chargebacks on the lab space in lieu of rent, does it cover electricity, does it cover if the research involves toxic or bio hazards, the cost of disposal?). Many of the private schools at the head end of the list are presitgious schools and in general they tend to pay more for administrators and such then a public university might (my sister worked both at a private university and a public one, and the private one paid much better as an administrator) and that could factor into it,and why is wellesley so much more expensive than Yale or Caltech? It would be interesting to see what it is at U Cal Berkeley and compare that against the other cal state schools.