Couldn't it be as simple as wanting to preserve some value for the fans who actually buy tickets?
In any case, if this footage is so valuable, 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?
In summary: unambiguously unlawful + powerful enemies = won't end well
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).
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.
They can but they'd get sued.