Well, I don't know the mechanisms, myself. I'm just saying that it seems like the most efficient thing to do would be to somehow guide the natural mechanisms already in place. Anything else would be reinventing the wheel.
But who's to say that a god wouldn't want to reinvent the wheel?
Anyhow, there's still a gap in the chain:
Supernatural agent -----> _______ -----> natural mechanisms -----> physical result
What fills in the blank? Our answer to this might imply other effects that can be tested for. We already know that whatever it is, it has natural, physical effects... otherwise, it couldn't "guide" natural mechanisms.
As an analogy, take evolution: it makes claims beyond beyond biology... for instance, it implies that the Earth is very old: at least hundreds of millions of years, if not billions. Using disciplines unrelated to biology, such as geology, this prediction was tested and found to be true.
That's the sort of thing I'm talking about. If a claim is true when it's explaining some effect we're interested it, its "side effect" implications will also be true when we go to examine them. It's hard for me to be more specific without a specific supernatural claim to deal with, but hopefully you get what I mean.
That's a judgment call, but I'm cool with it.
But isn't it a reasonable conclusion?
Also, doesn't it speak against the truth of the "generic theistic" model of God? A God that has absolutely no effects and does not interact with the physical universe in any way whatsoever doesn't mesh up with the theology of most mainstream religions, IMO.