I am not versed in that aspect but I would think that if they are considered employees and their scholarships are considered payment for employment then it should be subject to income taxes.
As for this dispute, my view as a former college athlete is that there are college athletes and then there are those who are not really collegians, they are just there to play a sport. Many are exploited, and get a raw deal. A starter at Alabama who doesn't go to class much and is not quite good enough for the NFL doesn't get the education end of the bargain and doesn't get the shot at the pros either. He may have back and knee problems that will start haunting him in his 40s and cause an early retirement and early death. That kind of player, which is a substantial part of the division 1 football and basketball players, should be able to get more of the huge revenues that are generated by his school's program. In my, free-market oriented, opinion.
Of course, the current system of big-time college sports is a sham anyway. It is not Syracuse or USC or Purdue playing another team, it is just a group of non-students brought to that school to compete against another team's non-students. They bring in someone who could not get into the school in normal circumstances, and the athletes often attend special classes set up for athletes, with professors who pass them if they show up, and they get a degree that is worthless at the end.
If it were up to me, college sports would be played by people already in the school for academic reasons. Dumb schools would generally be better than smart schools. Fine. Ivys can play each other; big state schools can play each other if they want. No one gets anything for playing a sport; they do it if they want to as recreation once they get to college. Meanwhile, the people who are not that interested in school can play in minor leagues and not have to pretend to go to school. They can make money and support themselves and work on their game for 2,3 or 6 years while they try to make the pros. The NFL would hate this (they would have to fund a minor league system), and the sports networks would hate this, so it will never happen. But I still don't understand why people care about a school team when what they are really rooting for is the ability of a school to convince 17 year old disadvantaged youngsters to go to their school and play for them for free, even though they are not going to get an education.