While it entirely possible that between one and two million fully automatic weapons were in private hands in the United States at the time of the passage of the 1934 act, that would have required that practically the entire production of German automatic weapons to have been transported home as souvenirs. Yet the German army did not go out of business and continued to use WWI production into the middle of WWII. For example, as near as I can estimate, German production of the Maxim did not exceed one-quarter million units, all heavy machine guns (which now would be called medium machine guns). They did get some submachine guns into production as well but I didn't check any of those numbers.
But perhaps I am rash in assuming that soldiers only brought home captured enemy weapons.
On the subject of these weapons, I do remember being startled when I noticed one such machine gun on inconspicious display in an office many years ago when I was in their on business. I didn't inquire if it was in working order but at least that one managed to cross the ocean. It was an air cooled version.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.