Then it wasn't a military issue weapon. The standard issue SG in Vietnam was the Remington 870 Express, a 12 gauge pump. The modifications weren't length but chokes, duckbills, stocks and camouflage. There were a few Winchester and Stevens but they were 12 gauge pumps too.
I don't know if my friend's shotgun in Vietnam was mil issue or not. I know he also carried a revolver that his folks sent him from the states. I believe it was a .357 and probably a S&W but it was years ago that he told me about it so I may have forgotten calibre and make. You are simply wrong about sawed off shotguns not being used by U.S. troops in war. Whether they are standard issue or not is irrelevant. They are legal and are used.