I'm fairly certain the NFL has licensing rights and prohibits any video reproduction of any kind so you could try to get away with it for awhile, but it wouldn't last long!

What is the legal basis that gives them this ability?

I believe a recording of a performance would be considered a derivative work under copyright law. As such what you're advocating is large-scale commercial copyright infringement against the NFL and the networks who pay it for exclusive rights.

In summary: unambiguously unlawful + powerful enemies = won't end well

To be a performance there has to be a creative element, not just a skill. Like wrestling for example, which is pre-scripted.

Otherwise someone jumping on a trampoline in his backyard could claim that he is performing and forbid the neighbor from recording him on a copyright basis (rather than a privacy basis - they are completely different laws).

I believe the stadiums as private properties can set rules on what is allowed to be brought in. Most ticket have a disclaimer on the back saying you can't film in the stadium but IANAL. It could just be FUD.

They can limit what you bring in - certainly.

But if you anyway do actually record I don't know of any law supporting their position that you are not allowed to transmit that recording.

>> why can't somebody with a good camera phone buy a seat in the nosebleed section, set up a tripod, and charge for the stream?

They can but they'd get sued.