Nah they're just fine. We don't really have an agreed upon definition of what a PDW is.
My personal criteria is that it needs to be concealable in a reasonably sized backpack/bag that can be transported and carried inconspicuously. Mostly it comes down to a persons individual needs and preferences. I personally wouldn't use a shotgun in that role but it seems there are some that do.
Mine is my Colt 11.5" 6933 upper on an Aero lower with a Law folder and brace.