Correct. Miller only held (perhaps incorrectly, too) that a short barelled shotgun was not a 'militia' weapon.
Despite that ruling, shotguns have played a part in military arsenals in virtually every war since WWI, from the trench brooms to the antipersonnel rounds of the M-79 and onward.
I'd love to get my hands on an AA-12. Not so oddly, it's a "short barreled" shot gun. Particularly deadly in urban environments for our Troops. An excellent back-up "militia weapon".