I've been thinking about this a lot lately. Whether we mean 'supernatural' in terms of religious miracles, or whether we mean it in terms of ghosts or other such events, I posit that the concept of the supernatural cannot exist.
Conjecture:
Anything with the label 'supernatural' which is found to be a real part of the physical world (let us say someone proves ghosts exist), then whatever is behind that must be underpinned by a scientific principle and must, therefore, be a natural occurrence (assuming that no technology is the cause).
Anything natural cannot be supernatural, and anything supernatural which is proveable is, by default, natural, meaning that the concept fo the supernatural cannot exist.
Discuss.
The whole premise is faulty. Your main arguing point is semantics, at best.
First, dimensional theory probably precludes any argument you can reasonably make. I'm no expert on it, but my flimsy understanding of it explains your reasoning (eg: if God exists on a higher dimension, He can reasonably and easily manipulate the lower dimensions that would appear "magical" and/or arbitrary to us lower dimensional observers). At some point, you'd probably have to transcend "nature" and enter some other realm of existence or creation, or whatever you want to call it.
Second, supernatural doesn't necessarily mean it's inexplicable through nature, that is, unobservable. Storms probably seemed supernatural to our prehistoric ancestors, but we now have reasonable understanding of why or how storms form and are expressed. It's not such a mystery, afterall. Heck, we can even scan for the change in conditions in order to accurately PREDICT when storms will form.
However, if I could wave my hand and make it rain, and I could do this at any time whenever I wanted, you'd be intrigued, no? That's "supernatural" for lack of a better term.
This is along the lines of your reference of turning water into wine. This is a different scenario. People shouldn't be able to do that. Similarly, raising someone from the dead after they have been dead for four solid days and begin to stink of decay should not happen, either. So if someone could do it, why can they?
Even if we could identify and observe the molecules changing in the process of water becoming wine, we wouldn't necessarily have the ability to reproduce the effect in the way Christ did it (He touches water and prays, it becomes wine; we'd have to do some other arduous "natural" task to achieve the same results). Like the dead guy coming to life, we could see how or why they came back to life (heart restarted, necrosis was reversed) -- we simply could not explain reasonably why it was able to take place when Jesus spoke the words for Lazarus to get up and come out of his tomb.
We can bring people back from death through adrenaline shots or CPR. But it's not the same thing, is it?
By your logic gravity is at best supernatural. We can observe gravity. We cannot reproduce it or even reasonably explain it. We surely cannot create it or manipulate it directly.
If a guy came along and could alter gravity around himself in order to levitate or crush buildings, we'd be intrigued. Even if we can observe the change in force, there'd be no explanation as to why he can manipulate it and no one else could.
In other words: concepts can exist. Supernatural is a concept. Therefore, the supernatural does indeed exist.