There are currently in excess of 265,000 permit holders for "destructive devices;" however, this number includes suppressors and sawed-off shotguns and rifles, as well as auto weapons.
I saw that TV show, too. Approximately half of the Browning M1917's & M1919's made are in civilian hands (there were about 64,000 made of each.)
The most reliable source I can quote on MG's being used in crimes reports that one LEO used a Mac to "grease a snitch."
I have often wondered how many people there are in this country who have great uncle John's old trunk in the attic which they've never opened-and which contains a Maxim MG, or other WWI souveniers.
It is estimated that returninig doughboys brought in at least 1 million guns as war trophies. While it is certain that many of these are the prosaic rifles and pistols of the era, it stands to reason that since no firearms laws were in effect in 1918, a good many of them were MG's. It also stands to reason that a good many of them are still around and still unregistered 'cause the current owner doesn't even know he owns it.
Shoot straight & make big holes, regards, Richard at The Shottist's Center