They bought them in Florida. As far as know it is not possible here in Cayman to get a permit today for a rifle of a hunting callibre. .22, 9x18 (9mm Luger) are the only callibers they allow. Untill recently a couple managed to get a permit for .223, but that got stopped. I do not know how it works in Florida to be frank, but I have (on asking a gun dealer) been told that all he needs is an adress and a few days. None of the guys is an US citizen. Cayman Islands and British. Some own houses there though.
To import a gun of any sort into the US is a nightmare unless you are a dealer, but difficult even then. My wife bought a Manurhin .357 Mag from the US. Took almost a year for the US dealer to get the export permit from France and import permit to the US sorted. The biggest problem was that the Frenchies sent over documentation that were not sufficient and correct for the US customs, they did this several times. The standard French papers were not what the US wanted. Nobody wanted to bulge.
What a world we live in....Bureaucrats and insanity rules.
Your friend who's a dealer was wrong. According to my dealer's handbook (yes I was a licensed C&R collector with dealer's privileges):
"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 reesiding in that State and has resided continuously in that state for at least 90 days prior to the purchase. An alien acquiring firearms from a licensee is required to 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 documentaion 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.
C.F.R. (Code of Federal Regulations, the federal law)"
[18 U.S.C. 921, 922(b)(3), (d) and (g) 27 C.F.R. 478.11 and 478.99(a)
All bold emphasis are mine. The point of it all being that after a period of 90 days (and having acquired a government issued photo ID such as a Driver's License) as well as a long term lease and job (which can only be gotten with a resident I.D. card; the "green card") an alien has essentially established permanent residency. The 90 day period is exactly the same as required foir a native citizen to establish residency in a new state (or even a new county or town) for voting purposes.
Furthermore the form you have to fill out when buying a firearm (A.T.F. Form 4473) has a series of questions the buyer must answer. One of said questions (number 15) specifically requires aliens to provide their U.S. issued alien number or admission number. Here's a link to the form
www.atf.gov/file/61446/download As you can see, there are some exceptions for properly documented sport hunters and a few others.
Regarding importing a firearm here I've only ever done it once when I returned from England. All I had to do was fill out the Customs Declaration; but that was a shotgun I had originally bought here and had taken out of the country with me to England when I was stationed there.