Still coming out the wire assigned to the church address, and that what the ip will be traced to, hence authorized by the church; as in "the church agreed to have this hot spot here"
What if they used the church bathroom? Maybe consider getting rid of those or at least installing cameras in them so you can be sure no one is doing anything unholy. Hmm, actually then who could view the footage to monitor things? I suppose you could only permit someone that was totally trustworthy, like the pastor? But what if he/she secretly enjoyed that? Maybe have a two person team view all bathroom footage? Make sure they pray first (and maybe put a camera on them, just in case. Can't be too safe).
You're missing the point. If someone brings the internet with them into the church and does X, the church is not involved. If someone comes to the church, connects to their internet connection and does X, the church enabled it.