In Chicago’s Chinatown, back when I used to eat there a decade or two ago, some of the less touristy restaurants had a menu in English and another entirely in Chinese. The Chinese menu wasn’t “secret” in that it wasn’t hidden, but it did have entrees like chicken foot soup that weren’t on the English menu and that non-Chinese were very unlikely to order (or even know about). However, if you weren’t Chinese but ordered chicken foot soup or the like they would serve you, once they were assured that that was what you really wanted.
Since your position is that people are horrible for ordering off-menu, wouldn’t it be nice to have a workable definition of what “off-menu” means so that people can know just how horrible they are? If you complain about someone’s behavior, it’s nice when that behavior is defined.