I used to work for a large company. "We" had to be careful, at least back when, to avoid restraint of trade issues with smaller competitors. A huge company can offer a grocery chain a "deal" on some product like say "Tide" if said company also puts "Always pads" on an end of aisle display. If you do this when some smaller operation has come out with a new sanitary pad, you might well be in for a fight with the guvmint. You can also just happen to drop your prices just as a new competitor enters the market.*
The NCAA is voluntary, but they also wield considerable power ($$$) and they could be seen to be preventing other schools from forming their own associations by for example locking up all the lucrative TV contracts ahead of time. Maybe.
What I know all of this could be summed up by saying "It's a tricky area" that makes lawyers wealthier.
*My favorite story was by the guy who started Formula 409. He was doing well enough to attract attention of a, um, large company who will remain nameless. Said large company developed it's own product and started a test market in Denver, CO. The Formula 409 guy saw this and pulled ALL of his product from the shelves in Denver. The large company had a HUGE test market result and then expended into the mountain states. The Formula 409 guy just before this dropped a two for one on his product in the mountain states. The test market expansion flopped, and the unnamed large company withdrew.