I had the same belief that the ser numbs are kept at the gun shop, not recorded during the background check.
I don't think I have ever heard a seller give out the serial number of a firearm I purchased over the phone during the background check phone call.
All the records stay with the FFL unless requested by an LE agency. Most are never even put in a computer, the 4473s are just stuffed into a file cabinet.
As far a the shotgun plug Dawico got, some dealers fill out and send in a warranty type of form to the manufacturer. The tracking came from the seller to Remington, did not pass through any government entity (other than the post office, LOL). Sometimes I have been asked to fill out those forms by the seller, and refused.