Not quite. The Constitution & BoR governs Federal activities. As such, anything the Federal does MUST be in compliance with the rules & restrictions governing the Federal.
So truth be told, the Federal shouldn't be able to regulate firearms insofar as the regulations relate to the 'Right of the people to keep and bear arms shall not be infringed'.
They could likely get away with (legally) not allowing certain models / brands / types to be sold in the US so long as they are allowing some models to be sold. The right pertains to private ownership & carry/usage.
The problem lies in the fact the Fed has not been following the rules governing it and we the people have given it a pass on its transgressions.