I read Miller in the epitome or digest, and scanned through the opinion, reading parts of it, and I agree with the point you made. The court made their remand of Mr. Miller (a common criminal caught with an NFA Class II sawed-off shotgun) hinge on the question of whether weapons like Miller's were "militia" weapons. The Court said no -- and the Court fibbed. Shotguns were widely used in the trenches in the Great War, so it erred on a point of fact.
The Court also erred in trying to divide personal sidearms by classifying them, and pretending to rule out the class to which Miller's weapon belonged, for the purpose of a) screwing Miller and b) upholding the NFA and providing the case-law test that Franklin Roosevelt wanted, and which he sent his Solicitor General to get from the unresisting and unrepresented, destitute felon Miller, whose lawyer had quit because Miller couldn't pay him. (Miller's partner was even more disadvantaged: he was dead.)
The language is simple enough: The right of the people to keep and bear arms shall not be infringed, and that includes sawed-off shotguns. The Court lied when they introduced a fictive, fabricated distinction.
There were other points and their sequelae, but that one is the one you were commenting on.
Not quite. The Court said there was no evidence presented either way in prior proceedings, the defendants were not present to say "well duh yes", the plaintiff didn't say anything, and the answer wasn't inherently obvious, so sent the case back to the lowest court for evidence gathering. By then Miller was dead and his pal copped a plea.