A foreign national here on a visitors visa can purchase a long gun. In most cases they are only required to have a hunting license. Laws are a little stricter on handguns.
An alien admitted to the United States under a nonimmigrant visa is prohibited from shipping, transporting, receiving, or possessing a firearm or ammunition unless the alien falls within one of the exceptions provided in 18 U.S.C. 922(y)(2), such as: a valid hunting license or permit, admitted for lawful hunting or sporting purposes, certain official representatives of a foreign government, or a foreign law enforcement officer of a friendly foreign government entering the United States on official law enforcement business.
[18 U.S.C. 922(g)(5)(B) and 922(y)(2); 27 CFR 478.11 and 478.32]
Having a valid hunting license would be reasonable for ammunition, but I have no idea why firearms are included. He certainly wasn't 'admitted' into the US for hunting, so that wouldn't apply.
You are correct. I was referring to the idea of a right to bear arms itself.
Actually, that goes back hundreds of years in British Common Law, which is the basis for US law. In our (US) case we 'froze' the protection of that right in time by incorporating it into the Bill of Rights. In the rest of the old Commonwealth they removed those protections over time until you have the sad state of affairs we see today.