Despite starting by talking about "college tuition" in general, this article looks at public colleges only. It doesn't even try to explain the tuition increases at private colleges, which if anything have been larger.
The public funding argument doesn't exist at private colleges. If private colleges want to charge through the roof, so be it. (Although perhaps we shouldn't be guaranteeing the loans if they're a luxury good)
It would be interesting to see more information breaking down the increases there to compare to the causes at public universities. I saw an article the other day that stated that private colleges have also been increasing their financial aid or scholarships per student. Maybe that eliminates any of the difference in price changes between the two.
75% of students attend public universities, so the case they cover is the modal case.