The basis of antitrust law is that we like competition. It promotes efficiency. It promotes innovation. It helps consumers. But what is the competition? Here, is it 32 teams competing among themselves? Or is the NFL one "umbrella business" and the competition is another (currently phantom) league?
It's an interesting theoretical discussion. Imagine if, say, the Lakers tried to schedule 100 games, not the usual 82 next season. Crazy, right? You voluntarily join a league and you're subject to league rules, even if it's to your economic detriment. But what if, say, Vitamin Water offers the Lakers millions as a sponsor; yet Gatorade is the official sports drink of the NBA?
In the American Needle case, the 7th circuit ruled in favor of the NFL. From Judge
Here's another interesting tidbit: