At one point she states "Heller allows an individual right for weapons that were in common use"
In fact Heller states:
HellerUnited States v. Miller...limits the type of weapon to which the right applies to those used by the militia, i.e., those in common use for lawful purposes.
...Miller’s holding that the sorts of weapons protected are those “in common use at the time” finds support in the historical tradition of prohibiting the carrying of dangerous and unusual weapons.
Heller is ruling about the carrying of dangerous and unusual weapons. Miller allows for weapons used by the militia... i.e. M9 pistols, M4 and M16 select fire rifles, etc and allows for the prosecution of "unlawfully, knowingly, willfully, and feloniously transport in interstate commerce ... 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"
US vs Miller
It is worth noting that Miller did not defend the case in court and short barreled shotguns are used by the military. No evidence was submitted in the legal proceedings.