A black person didn't. A white, English woman did. It's a perfectly cromulent phrase.
Maybe they need to edit the sentence for American audiences. Like they changed "philosopher" to "sorcerer". It's clearly confusing them!
those of us with a reasonable base of education know what a philosopher's stone is. The topic is even covered in basic chemistry classes as a historical component about alchemy. heck, Full Metal Alchemist didn't have to dumb it down. Don't confuse Hollyweirdisms for americanisms.
"Hermione's white face stuck out from behind the tree" most clearly tells me she was seen because she is pale and the night is dark and her head was sticking out from behind a tree.
It does little to imply fear in that sentence. Had she been black, it would have been the whites of her eyes and teeth that gave her away, the rest of her face blending in more readily into the darkness, regardless of how pale she was feeling.
Rowling forgot she wrote that little sentence, and made a declaration that Hermione is raceless in the book, when had she really envisioned a non-white girl and envisioned the scene in actuality, would have come to a different description.
It may be perfectly cromulent, but the glove does not fit. the probability that an author would describe a black character hiding behind a tree with their head sticking out as "white face" would be one of ignorance to the actual visuals of the scene.
Basically, go get a white and black friend, wait until night, and take some pictures of them hiding behind a tree with their head sticking out. Heck, film it. Then draw a gun on them, to get the blanched fear look.
Pretty sure you won't be using the word "white face" to describe the black friend (even without the gun, that's just dangerous), except to be contrary.