You left out a couple of key facts - like they were charging for the party and using some copyrighted material to promote it.
NFL PARTY RULES
For groups that want to host Super Bowl parties -- other than sports bars and businesses that normally show televised sports -- here are rules the NFL says must be followed:
• No admission fees (even to pay for snacks).
• Only one television (55 inches or smaller).
• No use of the words "Super Bowl" in promotional materials.
• No exhibition of the game in connection with events "that promote a message."
Source: NFL
The key word here is groups - if you invite twenty friends over to watch the game on your 72" flat panel the NFL isn't going to knock down your door and bust up your party.
Those are 'NFL rules' (not 'copyright law' as previously stated)? How are those enforceable? What licensing agreement is an individual engaging in when they turn on a set to show a broadcast on the open airwaves? What legal premise gives the NFL power of enforcement and an ability to attach compulsory licensing to free broadcasts (other than the threat of legal intimidation through civil prosecution)? The church isn't engaged in reproduction of the materials (DVD, re-broadcast, or anything else).
The were initially notified because they were advertising to come watch the Super Bowl and listing the admission fee. A big no-no. Also, they were advertising the testimonials of NFL players.