I don't really, for the moment, have a problem with anything else but the MC's initial decision to reveal the knight is from another, magical universe. Since her magic allows her to speak any language, they should have claimed she's from Russia or North Korea (in which case she would be an abducted foreigner), or something equivalent, from extraordinarily dire circumstances in any case. That would have given an excuse to making it extremely difficult to verify anything. It would have also made it sufficiently troublesome to try to deport her (where?). She could have also gone through a more mundane health check, which could have still been decently thorough. In any case, since she wasn't a vagabond but was basically working for the MC, the government might not have been too interested. But I guess that wouldn't have made such a dramatic story.