I agree it is not a for-profit institution, but I assume the commentator is using "for profit" in the colloquial manner for "non-profit that is charging exorbitant amounts".

Pedantry and HN - name a more classic combo

I think the distinction is relevant if we're discussing whether they deserve non-profit tax breaks.

"Their tuition is expensive" isn't a good reason to exclude them from the tax break. "They are abusing their non-profit status to basically operate as a for-profit corporation" would be a good reason, but I don't think it's true.

"Their tuition is expensive" – i.e. their fee structure excludes most American families from even having the university in their child's consideration set – is a valid reason to have them pay taxes, actually.