Do Wizards Have to Follow International Travel Regulations?

From the original Harry Potter series and the supplemental material, we know that wizards as portrayed in the series are a global phenomenon, that magical beings from different countries interact with each other, and that they are subject to different laws than the non-magical population.

Hell, we even know that very few countries have their own magic training high schools. So we can conclude that it is not uncommon for students to attend magic school in a country that they are not a resident of. In the non-magical world, doing such a thing requires obtaining a student visa: a process that is not difficult, per se, but is very bureaucracy-heavy, especially if the applicant is a minor. I know this because I have both applied for one in college and recently worked as a visa clerk. One of the required documents is an acceptance letter from the school. Since the secrecy statute is a thing, I doubt any wizard high school would be cool with students showing their actual acceptance letters to government authorities and even if they did, the most likely reaction would be, "haha, this is funny. We're denying you."

That brings me to an alternative hypothesis: the schools give all international students a decoy letter enabling them to lie to the government to get their student visas. And since they're magical, they can pull it off without being caught. This seems like a likely solution, until we remember that wizards have their own governments, which means that they might have the authority to issue visas independently from the muggle government. They could probably make them look enough like muggle visas that border agents would not suspect a thing.

Then there's my other alternative hypothesis: magical beings could not give less of a fuck about international travel regulations and can use their magic to skirt around the law. Characters in the series are shown using magical instant-travel techniques including but not limited to floo powder, portkeys, apparition, and whatever the hell you'd call the wall between platform 9 and 10. There is no mention of whether or not these things are regulated. That's probably because the series was originally intended for children who don't notice these things, but has that stopped me from poking holes in it so far? Of course not!

It does mention that fireplaces that use floo powder have to be part of a network, making it the easiest of the products to regulate. But the other ones? Regulating them would likely be difficult, even with the fantastic powers. If there is no distance limit on these methods, they could allow magical beings to travel internationally without taking a plane or train, which would in turn allow them to avoid passing through customs. If they are caught by border agents during their trip, they probably use something similar to the Doctor Who'verse's "Psychic Paper," which immediately forges whatever credentials a traveler with inhuman powers would need. I cannot recall a mention of such a product anywhere in the Harry Potter series, but the characters are never really in a situation where they would need it. So it could still exist?

It is not difficult to poke holes in a carefully-constructed fictional universe that is only viewed through the eyes of a narrator who is not always reliable, especially when the universe is supposed to exist alongside our own. We all know that our world is complicated, so it makes sense that we expect fictional worlds to be just as complicated, especially with regards to things that we know more about than the "average person." I can't say which of the hypotheses I've proposed are the most likely, but if JKR wants to respond, I'm all ears.