This is why there is a NFA registry-
§5841. Registration of firearms
(a) Central registry
The Secretary shall maintain a central registry of all firearms in the United States which are not in the possession or under the control of the United States. This registry shall be known as the National Firearms Registration and Transfer Record.
https://www.gpo.gov/fdsys/granule/US...nt-detail.html
https://www.gpo.gov/fdsys/pkg/USCODE...tI-sec5841.htm

This defines what a NFA firearm is-
§5845. Definitions
For the purpose of this chapter—
(a) Firearm
The term “firearm” means (1) a shotgun having a barrel or barrels of less than 18 inches in length; (2) a weapon made from a shotgun if such weapon as modified has an overall length of less than 26 inches or a barrel or barrels of less than 18 inches in length; (3) a rifle having a barrel or barrels of less than 16 inches in length; (4) a weapon made from a rifle if such weapon as modified has an overall length of less than 26 inches or a barrel or barrels of less than 16 inches in length;
https://www.gpo.gov/fdsys/pkg/USCODE...tI-sec5845.htm

This has generally been interpreted to mean by definition it is only a NFA rifle if it has a barrel less than 16 inches or overall length less than 26 inches. It doesn't meet the definition of a NFA rifle if the barrel is longer than 16 inches. By definition you register a rifle, not a receiver.

My previous post quotes from a FAQ from two years ago that seems to back this up. I'm not Authorized so I can't tell if they have changed their minds on the way it is done now.