The "good private universities" may be "non-profit" in some strict sense, but in the case of the big Ivies (e.g., Harvard, my alma mater), they could be described as a hedge fund with, oh, yes, by the way, a school attached, or, alternatively, as a huge Federally-funded research institution.

The educational part seems to be a facade for the big money/big institution part.

(Bitter much? Sure. ;-)