Natural science does appeal to the supernatural, because it appeals to nature and nature is supernatural. Nature is an aspect of divine art allowing things to act for themselves; it is a way of being open to divine action.
“Nature is supernatural”, i.e. not because it is included among supernatural persons but because it is a proper effect of them, the way that a Chevy is American or a Corona is Mexican, not because either is a citizen or a member of that polity but because it is something they made. I’m American, Obama is American, Clinton is American, etc… one can run through the whole census and never hit “Chevy”. In the same way, “supernatural” marks off a community of persons (gods, saints, angels, etc.) and we can run though the whole census and never hit “nature”.
Any time one tries to parley something out of methodological naturalism, they’ll need to say more than that science never appeals to supernatural causes, which is obvious, they have to prove that it doesn’t appeal to supernatural effects, which is much harder to do. Obviously, Naturalism is just as refuted if one admits supernatural effects as if they admit supernatural causes.