Good info in your post. My comment was more tongue and cheek. As I am in no way gullible enough to believe there is no database accessible by the fedsNo. A Form 4473 can legally be used to get information when a gun is retrieved by LE that has been used in a crime or retrieved under otherwise abnormal circumstances. The procedure is the LE gets the S/N, contacts the manufacturer, the manufacturer tells which supplier sold the gun, and to whom if there is a warrant - Then there is also the case when the seller (keeper of the Form 4473) will voluntarily give up the information to LE.
In this case, it isn't a 'database' situation - there is a process. But I am not stupid and there's a high probability that the FEDS have been compiling illegal databases for years.