It is illegal for a foreign national without permanent residency to take possession of a firearm, except for hunting. They can purchase and have it shipped abroad to their home country, with the proper export paperwork. They can rent one for use at a tourist rental range. They can buy one for the purpose of hunting.
He was also under 21. He could not legally purchase a handgun from a gun dealer.
There have been several cases of college students on student visas being arrested for attempting to purchase firearms. No green card, no hunting license, no gun. He was in violation of the law. There was no special “oh shit we gotta make up something to charge him with” in his situation.
None of which changes the fact that the sole reason he was investigated in the first place was because he made a threat to a classmate that he was going to shoot up the school, and she felt that it was not a joke.