I studied copyright law in college. This is major bull malarky. The game is broadcast on a network that is free to receive if one purchases the required equipment to pick up the signal. The copyright owner, in this case CBS and the NFL, have been compensated for their product's broadcast. Handsomely. There is no way this stance will hold water in a court room if the opposing attorney has even a passing familiarity with copyright law.
Now, rebroadcast is another issue. I assume charging a fee for watching the broadcast (cover charge at a bar) would also be a valid issue. Recording it and selling copies is of course right out.
Greed. Plain and simple. They make beaucoup millions from advertising, another buttload in merchandising and licensing fees, and untold revenue from cable outlets like ESPN paying for the rights to air highlight clips, which can only be shown after a certain amount of time beyond the actual event aired on the network. The NFL is the most popular sport in America. This will bite them, hard.
