Only if you think God cannot use natural means. The two are not mutually exclusive.
Yes they are. In your scenario it's a supernatural explanation.
To say some supernatural agent is "using" a natural mechanism is uninteresting. In that case, we can always insert some undetectable supernatural thing behind everything we see. Einstein's GR explains the orbits of planets naturally. We can accept curved space-time, then insert Planet Fairies that push the planets in their orbits, and I guess the naturalist cannot "prove" there aren't Planet Fairies. But again, that's an uninteresting claim. It takes advantage of how malleable the concept of God is.