I don't disagree with you, but that's not what people usually mean when they say "supernatural" and this is what I was pointing out. Usually, it's taken to mean a bit of literally impossible nonsense that happens anyway.
You're right - once something actually happens it falls under the domain of science. Most people don't realize that, or they don't accept it.
I guess I'm saying that actual magic wouldn't be merely indistinguishable from sufficiently advanced science, it would be sufficiently advanced science. Magic is just the flashier, stagier term for the same thing.