A lot of the FFLs have the guns on their books, and get all excited about nothing.  All they have to do is enter "sold as antique" in their bound book, case closed.  There's no good reason for you to have to go through and pay another dealer, no reason for a background check either.

By the way, it appears your purchase has had the barrel free floated, like one of my 92/96s has had done.  I'll bet it will be a very accurate shooter.