A question for... LEOs? Gun store owners/employees?

[spqrzilla]

The answer to your question is in the ATF FAQ. A non-resident alien can buy a firearm only if they've been resident in the US for 90 days, and have a hunting license.

Q: May aliens legally in the United States buy firearms? An alien legally in the U.S. may acquire firearms if he has a State of residence. An alien has a State of residence only if he is residing in that State and has resided in a State continuously for at least 90 days prior to the purchase. An alien acquiring firearms from a licensee is required to prove both his identity, by presenting a government-issued photo identification, and his residency with substantiating documentation showing that he has resided in the State continuously for the 90-day period prior to the purchase. Examples of qualifying documentation to prove residency include: utility bills, lease agreements, credit card statements, and pay stubs from the purchaser’s place of employment, if such documents include residential addresses.
See also Item 5, “Sales to Aliens in the United States,” in the General Information section of this publication.
[18 U.S.C. 921, 922(b)(3), (d) and (g), 27 CFR 478.11 and 478.99(a)]

This link here from the ATF explains the rules for non-immigrant aliens which changed in April of 2012. There you see the requirement of a hunting license for a non-immigrant alien to take possession. However, I do think that this requirement applies to a rental within a firing range by a tourist. I think some range has misapplied the rules.

This exception exists to allow a tourist to come to the US for the purpose of hunting.

Note to return to their home country with the firearm is going to take an export license.