Correct. If it had, they would only needed to have noted that Miller was not a member of any militia, and "case closed". Instead they strained at gnats to define "arms". But in so doing, they implied that ownership of machine guns, grenades, Claymore mines, and even heavy weapons, was protected as their "possession or use ... at this time has some reasonable relationship to the preservation or efficiency of a well regulated militia". In fact it's really too bad Miller didn't have a Thompson, as taking judicial notice that those had a military purpose would have been completely justified, and the Court would have been laughed off the Bench if they had ruled that the original judge should not have taken such notice.
The Brief filed by the United States argued the Collective Rights theory, but even this Court who strained to find a way to uphold the National Firearm Act, did not mention it in the decision. The Court waxed eloquent over the meaning of militia though.
Below is the summary of the argument contained in the Government's brief.
summary of argument The Second Amendment does not grant to the people the right to keep and bear arms, but merely recognizes the prior existence of that right and prohibits its infringement by Congress. It cannot be doubted that the carrying of weapons without lawful occasion or excuse was always a crime under the common law of England and of this country. In both countries the right to keep and bear arms has been generally restricted to the keeping and bearing of arms by the people collectively for their common defense and security. Indeed, the very language of the Second Amendment discloses that this right has reference only to the keeping and bearing of arms by the people as members of the state militia or other similar military organization provided for by law. The "arms" referred to in the Second Amendment are, moreover, those which ordinarily are used for military or public defense purposes, and the cases unanimously hold that weapons peculiarly adaptable to use by criminals are not within the protection of the Amendment. The firearms referred to in the National Firearms Act, i.e., sawed-off shotguns, sawed-off rifles, and machine guns, clearly have no legitimate use in the hands of private individuals, but, on the contrary, frequently constitute the arsenal of the gangster and the desperado. Section 11, upon which the indictment was based, places restrictions upon the transportation in interstate commerce of weapons of this character only, and clearly, therefore, constitutes no infringement of "the right of the people to keep and bear arms," as that term is used in the Second Amendment.
Do you have a link to the whole brief?