They're paying for epaulets. I took graduate courses at a "local" state university before starting a full-time program at a big-name-top-low-number private school. The private school was not a better education, but it was undoubtedly better for my career because of the "epaulets."

>watch the classes online and self-study, and pay a nominal fee to exam?

We are already far past the point on using exam scores as a basis for admissions. Many of the Ivies, famously say every year that they could fill their incoming class with students with perfect scores and perfect GPAs many times over forcing these schools to consider other factors. The US DoE says there are 16.9m undergrads, assuming ~4m are freshmen, the top 1% is 40,000 students. The Harvard freshman class size is 2000 students. At this point its only natural, according to the "market", that people would be paying for slots.