MP40??

You are correct; the Japs didn't use the MP-anything. They DID manufacture their own SMG but it was built in such low numbers so as to be inconsequential. It also fired an anemic cartridge, to boot.

MP-38s and -40s abounded in Hollywood prop houses and in 1959, nobody was the wiser and if they did know, they probably didn't care like we do today.

If you are a firearms and movie nut as I am, there is a great website called IMFDB.com; the Internet Movie Firearms Database:
http://www.imfdb.org/index.php?title=Main_Page