In this case he said he was buying it for somebody else BEFORE he bought it. We have two sets of laws to consder ~ AZ and US. Somewhere in there is the idea that you can't go around acting as a straw purchaser ~ and some have noted the law ~ which law? ~ says you may buy for personal use ~ but isn't this what ATF was killing hundreds of Mexicans by doing?
I think Kelly is showing us that existing laws, rarely enforced against high ranked politicians, do keep straw purchasers from using loopholes to buy firearms for other than personal use.
My reading of the statute leads me to believe that, unless Kelly made his "false" statement with the intent to transfer the firearm to someone who legally cannot possess it, then there is no violation.