Ah, yes, but therein lies the problem and is why the NCAA had it's head handed to it.
The colleges and NCAA created this euphemism called a "student-athlete" based on an argument of retaining "amateur status"...frankly, this has been a brilliant, legal, sleight of hand strategy which obviously worked for awhile. Interesting that the "amateur status" only applies to and limits the compensation of the "student athletes"...never anyone else around the sports program (e.g., athletic department, coaches, trainers, etc...).
However, the fundamental issue legally relates to price fixing which stems from the undeniable monopoly the NCAA has thanks to "cooperation" by all the universities which has created a system where the "student athletes" are compensated at much lower levels than a free market would otherwise create (just look at what players could previously make overseas or the obvious gap between the billions generated and what the "student athlete" actually receives in terms of tuition). Several justices hit at the price fixing aspect but Kavanaugh highlighted the hypocrisy very well when he said “schools are conspiring with competitors to pay no salaries to the workers who are making the schools billions of dollars, on the theory that consumers want the schools to pay the workers nothing. That seems entirely circular and somewhat disturbing.”