Nope. Not true.
The registered sear is the machine gun. The gun is not an imported machine gun, as neither is an HK-94 imported in 1998 and later converted to an MP5 with a registered "conversion part." Likewise, the 1968 GCA banned imported machine guns, but thousands of semi-auto UZIs were imported and converted to full auto with registered receivers (by class-IIs before 1986) or registered bolts (by anyone after May 19, 1986).