"High test scores often grant college credit at a public university – which means, very tangibly, needing fewer credits and tuition dollars to graduate – or a “you took a hard class” gold star (though no credit) at a private university."

Every private (US) university I applied to was willing to offer AP credit, given a high enough test score. The vast majority of my (private US high school) peers took AP exams, went to private universities, and received credit for their AP classes. One of them earned enough AP credit to enroll at Harvard as a sophomore.

I've never heard of AP exams being a "Public Universities Only" thing.