> if that's actually the case, how about put a small sign by the button? but is it really that hard to remove or disable the button?

These days, I think it would suffice for the local/national (depending on the scope) government to announce that pedestrian lights buttons are no longer working because $reasons. Rebroadcasted by media, it would reach many people, and anyone else would know where to look for answer, if they become interested in the question.

There's no real need to lie. It could be as simple as a tweet.