It's not the fake references that constitute cheating, but any plagiarization that might have happened beforehand. E.g., if all you used was what you remembered from lecture or other courses, then you needed to cite the lecture or the other courses, since that's where you actually got the information.
But, if I were Notre Dame, I would first tell him that is not his decision to make, and secondly I would have to question if I ever want him back.
We're talking about the football team and coach Kelly, but is he the one who decided on the punishment and second chance or is he just following what the academic side of the university has laid out? Did Golson get kicked off the football team for cheating, lose his scholarship, so have go somewhere else, or, the more likely scenario, did the university expell him (in which case he's off the football team) and now are going to allow him to come back and once he's a student in good standing, he can play football again.