I think there may be a problem with the word "magical" in this context, just like there is a problem with nature-worshipers talking of "supernatural powers".
If we've made a science out of it, no matter how advanced it is, it's not magic — e.g. if telekinesis was possible, it would have a scientific explanation and be a natural power — which bares some similarly to the way things are called "artificial intelligence" when they're impossible, only to be reduced to "trivial" when someone makes a machine do them: Chess, Go, having a large vocabulary or knowing many languages, being good at arithmetic or being able to do calculus at all, writing music or news stories, trading on the stock market — all things that used to be synonymous with genius, yet all done by machines we don't call intelligent.
Not so much an assumption as a reasonable guess. Is it logically possible that there's something magical about human brains? Yes.
But there are countless examples of things we thought were magical historically, and, as far as I know, exactly zero that we've ended up concluding actually were magical, and a large number that we're pretty confident aren't at this point.
The smart money here is on "no, the human brain isn't magical."