From "Instructions to Transferor/Seller" on ATF form 4473 (the long ol' background check form) subsection 2:
"Sale of Firearms to Legal Aliens (Part 1): A buyer who is not a citizen of the United States must provide additional documentation (beyond a valid government-issued photo identification that contains the buyer's name, residence address, and date of birth) to establish that he or she has resided in a State continuously for at least 90 days immediately prior to the date of the sale. See definition 7. Examples of appropriate documents to establish State residency are utility bills from each of the last 3 months immediately prior to the sale or a lease agreement which demonstrates 90 days of residency immediately prior to the sale."
Definition 7:
"State of Residence: The State in which an individual resides. An individual resides in a State if he or she is present in a State with the intention of making a home in that State. (skipping some non related material here) . . . An alien who is legally in the United States is a resident of a State only if the alien is residing in the State and has resided in the State continuously for at least 90 ndays immediately prior to the date of sale or delivery of a firearm."
From Important Notices #4:
"Generally, 18 U.S.C 922 (the Brady Law) prohibits the shipment, transportation, receipt, or possession in or affecting interstate commerce of a firearm by one who: (skipping more non related material . . . ) has renounced his or her U.S. citizenship; is an alien illegally in the United States or a nonimmigrant alien; or is subject to certain restraining orders.
EXCEPTION 2: A nonimmigrant alien is not prohibited from purchasing, receiving, or possessing a firearm if the alien: (1) is in possession of a hunting license or permit lawfully issued in the United States; or (2) has received a waiver from the prohibition from the Attorney General of the United States."
Definitions #8:
"Nonimmigrant Alien: An alien in the United States in a nonimmigrant classification. The definition includes, in large part, persons traveling temporarily in the United States for business or pleasure, persons studying in the United States who maintain a residence abroad, and certain foreign workers. The definition does NOT include permanent resident aliens."
SO, if you are not a citizen of the US, but a legal alien, the store is in it's rights and actually required by the ATF to ask for additional proof of residency. If you are a resident of the US, none of the above references apply to you and you should only need a valid Drivers License or CWP with proof of age.
Hope that helps some.