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).
It may sound trivial, and I doubt the NFL cares if some Baptist Church makes a few bucks from the game, but if they allow them to do it, they would have to allow everyone to do it.
You've asked some excellent questions. I wonder if NFL rules say anything about bookies taking bets on "the Big Game."