Private buyer sale has no background checks. Just go to a gun fair.
I live in Chicago, IL - I'm told that if I were to go to a gun show in Indiana, I'd be asked on the door to show ID. When I pulled out an IL state ID, I'd have my hand stamped, and then any gun I bought would have to be shipped to a registered gun dealer in IL for me to pick up there. That's how it's meant to work, although I'm sure it doesn't always go by the book, but a bearded muslim trying to buy an AR-15 would probably be made to play by the rules.
My point about the WV address thing is that he could actually play by the rules, it would take a month or two, but he could fully legally get everything he wanted, regardless of where he really lived. Thankfully he didn't bother