Hm. High heels are normally mandatory for women in Japan (in lots of companies) but I guess if she's not in a position where outsiders might see her, that they can be more lenient. (Like how western companies might require suits for all office workers, except the IT department who are supposed to be invisible anyway).
But if so, then her lack of high heels (and not the height that comes with them) might be why she was mistaken for an intern.