Are you claiming that Heller III did not hold that challenged gun laws are to be tested with "intermediate scrutiny" rather than the "strict scrutiny" the NRA demanded? (Do you understand the difference without using google?). That they did not uphold gun registration requirements?
I haven't read Heller III, but then, I'm not the one accusing someone else of not understanding constitutional law. How about you provide quotes backed by citation to the portions of Heller III that you say the author misunderstood?
A few notes on Heller I:
First, Heller made explicitly clear that the "arms" described in "right to keep and bear arms" were not military weapons.
"Before addressing the verbs "keep" and "bear," we interpret their object: "Arms." ....The term was applied, then as now, to weapons that were not specifically designed for military use and were not employed in a military capacity." District of Columbia v. Heller, 554 U.S. 570, 581 (2008)
Second, Heller explicitly limited Miller and in doing so expressed surprise at the notion that Miller should be read to overturn laws barring ownership of military weapons like machine guns:
We may as well consider at this point (for we will have to consider eventually) what types of weapons Miller permits. Read in isolation, Miller's phrase "part of ordinary military equipment" could mean that only those weapons useful in warfare are protected. That would be a startling reading of the opinion, since it would mean that the National Firearms Act's restrictions on machineguns (not challenged in Miller) might be unconstitutional, machineguns being useful in warfare in 1939. We think that Miller's "ordinary military equipment" language must be read in tandem with what comes after: "[O]rdinarily when called for [militia] service [able-bodied] men were expected to appear bearing arms supplied by themselves and of the kind in common use at the time." The traditional militia was formed from a pool of men bringing arms "in common use at the time" for lawful purposes like self-defense. "In the colonial [625] and revolutionary war era, [small-arms] weapons used by militiamen and weapons used in defense of person and home were one and the same." Indeed, that is precisely the way in which the Second Amendment's operative clause furthers the purpose announced in its preface. We therefore read Miller to say only that the Second Amendment does not protect those weapons not typically possessed by law-abiding citizens for lawful purposes, such as short-barreled shotguns. That accords with the historical understanding of the scope of the right, see Part III, infra
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District of Columbia v. Heller, 554 U.S. 570, 624-25 (2008) (citations omitted)