Regardless of how one feels about the myriad NCAA rules, the "Principle of Amateurism", Rule 2.9, is defined succinctly in the manual as:
"Student-athletes shall be amateurs in an intercollegiate sport, and their participation should be motivated primarily by the physical, mental, and social benefits to be derived. Student participation in intercollegiate athletes is an avocation, and student-athletes should be protected from exploitation by professional and commercial interests."
Of course there are many pages of rules that build on this principle and all kinds of interpretations of those rules, and I won't get into those here. If you're really interested read Bylaw 12 of the manual.
If Mary Cain, or any runner, is not interested in being a part of the NCAA system they are free to accept prize money. This is no different from any other sport that the NCAA has competition in, young golfers or tennis players are free to accept prize money, but of course once you do your ability to be a part of a college team, get a scholarship, etc, ends. And in many cases because you're dealing with decisions that could be made by a minor, sports have built in oversights that don't allow that minor to accept prize money.
To me, this is another of those rare cases where an athlete in a smaller sport is hurt due to the need to make an across the board rule that works for football, basketball, etc as well as track and all the other smaller sports.