Standing? This is the first time you brought up a standing issue.
How are they not "employees?" They perform a service and get paid in return through tuition, books, room & board. If they don't perform their service to the university, they don't get paid through tuition, books, room & board.
If you mean standing to negotiate their scholarship, they are a party to the scholarship, so they damn sure do have standing. The problem is the NCAA has it's overbearing regs on what can and can't be provided, which prevents the athletes from negotiating benefits. So these players don't have the freedom to seek the employment that they would be entitled to, and they don't have the freedom to negotiate the terms of the scholarships that they receive in return for their services. They also haven't had the freedom to even control and be compensated for the use of their likeness in video games, merchandising, etc.
Baseball players and hockey players have the right to be drafted right out of high school, and if they CHOOSE and the teams that draft them think they are good enough, they can play in the major professional ranks right then (See Valeri Nichushkin and Seth Jones). If they CHOOSE, they can play minor league baseball (associated with MLB) and begin working their way up the system.
NFL and NBA are really the only leagues who do it this way, which forces the athletes into a situation where their services are exploited for peanuts. You can say they get tuition, room & board, books, but they don't get money in their pocket. If they want to go grab dinner at McDonald's, you better have parents who pay for it, or go beg for the money. Get a part-time job? Yeah right, your full-time job is football or basketball.
I agree with that too. The leagues shouldn't be restricting anyone from coming into the league if their skills are worthy. There have been challenges to that, and there will be more.