All paper records are kept by the FFL. The only thing the Federales get a type of gun and # of them purchased at that time. They have to go looking to find anything else.
Do they keep records of background checks? Yesno. (No one really knows for sure, but do you trust them????)
The truth is you're the weak. And I'm the tyranny of evil men. But I'm tryin', Ringo. I'm tryin' real hard to be the shepherd.