From Reason:

So people who are on short-term trips from a Visa Waiver Program country (most European, East Asian, and Pacific democracies, plus Brunei and Chile), or countries as to which we have similar visa-free entry rules (Canada and Bermuda, I think), are not forbidden by federal law from renting a gun at a shooting range, or even buying or borrowing a gun to keep at their temporary home. But if they’re tourists or short-term business visitors from, say, China or India or Israel or Mexico or Brazil — trips for which a visa is required — then they are so forbidden; likewise if they’re here for an extended stay as a student or a business traveler.
[4.] What’s more, if you take someone to a range knowing that they are, say, a U.K. citizen here on a student visa, or an Indian citizen here for a short trip, you are yourself likely committing the crime of aiding and abetting that person’s illegal gun possession, or of conspiring with that person to illegally possess a gun. And that’s so even if you don’t know the conduct is illegal, so long as you know about the person’s immigration status.