It has nothing to do with Neilsen ratings and everything to do with federal copyright law. If the NFL granted the church a royalty-free license for such an event, not only would it be setting precedent that every church could ask for such a freebie, but the NFL would also be breaking its contract with whatever network is broadcasting the SB this year.
Trust me, this isn't the only time this has happened. The NFL, NBA, MLB, NHL, et al. send out hundreds or maybe thousands of cease-and-desist letters every year. There's nothing out of the ordinary about it.