well, technically a touhou character can have any sort of background since zun doesn't provide it, as long as the player can justify it somehow.

think of touhous less as individual characters, but more as original characters, with a basic mould already provided?

there is no true 'canon' interpretation of a character, tbh. except maybe reimu/marisa/whoever else that pops up in 3 games or more. and even then the background can still be whatever the fuck else the player wants it to be.