Here is what SCOTUS said (link to opinion and briefs) ...
In the absence of any evidence tending to show that possession or use of a "shotgun having a barrel of less than eighteen inches in length" at this time has some reasonable relationship to the preservation or efficiency of a well regulated militia, we cannot say that the Second Amendment guarantees the right to keep and bear such an instrument. Certainly it is not within judicial notice that this weapon is any part of the ordinary military equipment or that its use could contribute to the common defense. ...We are unable to accept the conclusion of the court below and the challenged judgement must be reversed. The cause will be remanded for further proceedings.
It seems to me that the holding of Miller is that if a weapon has a military use, and both short barrel shotguns and machine guns emphatically do have such purpose, then it is unconstitutional to so much as tax their acquisition and possession. "Any part of ordinary military equipment" is yet another category of arms that the Miller case held as out of reach of regulation.
The Miller case was subsequently read for the OPPOSITE of what it says, by Circuit courts who were asked to uphold subsequent convictions.
Circuits courts also read the Presser case for the OPPOSITE of what it allows states to do. It's easy to do - just cherry pick a sentence out of any opinion, and assert this is the principle.
Presser stands for the proposition that the right of the people to keep and bear arms, whatever else its nature, is a right only against the federal government, not against the States.Bach v. Pataki, 408 F.3d 75 (2d Cir.2005)
the states cannot, even laying the [2nd amendment] out of view, prohibit the people from keeping and bearing armsPresser v. Illinois, 116 U.S. 252 (1886)
Plenty of people blame the Presser case for what subsequent courts did with it, and the same is true with the Miller case.
When it comes to the right to keep and bear arms, the courts are bald-faced liars.
I was being a bit sarcastic but ultimately the USSC dropped the ball on Miller. Yes, lower courts allowed people to then lie about the case making it even worse. Had the USSC done it’s job correctly it never would have come to that.