This fails on several grounds.
First, there's the grammatical:
A Well-regulated Militia, being necessary to the security of a Free State, the right of the people, to keep and bear arms, shall not be infringed.
"Look," says the person advocating limitations on RKBA, "it says "Well-regulated militia."
Let's consider a different sentence, exact same structure but using different nouns:
Sweetened-condensed milk, being necessary for a good Key Lime Pie, the right of the farmers, to keep and raise cows, shall not be infringed.
Anyone want to argue that this statement means that the right to keep and raise cows is being confirmed on sweetened condensed milk? No? Then no more does the Second limit the right only to the Militia.
Next we have the problem of definitions. Much is made of the term "well-regulated Militia" and consider that only the National Guard qualifies. However, as I demonstrate elsewhere, to the people who wrote and ratified the 2nd Amendment, the Militia was the whole of the people capable of bearing arms. Back then it would have been all white males between the ages of 17 and 45. Today, we'd drop the limitations on race and sex (particularly as the Secretary of Defense has just directed that women be permitted in all combat fields in the military. So the Militia is the people and the people are the militia.
The Militia Acts of 1792 underscore that. The requirement that every household--every household--be required to keep arms and a certain amount of ammo and other supplies on hand simply emphasized that the militia meant the whole of the people, all of the people, not just those drawing government paychecks.
Then there's the historical argument. The idea that the 2nd is only limited to government militias being a "new" interpretation is preposterous. Consider the Dred Scott decision. On giving the reasons why they did not extend full citizenship to "The Negro Race": If they did it would, among other things, grant to them the right "and to keep and carry arms wherever they went." You can think that Dred Scott was a bad decision. I do. But it is utterly clear that at the time of the decision the court considered RKBA to be an individual right, not one limited to government troops. That's 1857. Hardly something recent.
It's the idea that the 2nd only limits RKBA to government bodies that's the new one. It first springs up in the Miller decision where the weapon in question--a short barreled (i.e. "sawed off") shotgun was considered regulatable because the court did not have "legal notice" that said weapon had a militia utility. Note that this wasn't a question of Miller (who was not present, having died before the case came before the Supreme Court, and only the government's side was represented) being in a government militia, but whether the weapon was militarily useful (it was--such weapons had been in use in World War 1 as "trench brooms", but with only the government side presented there was nobody to present such evidence to the court, thus no "legal notice"). Repeating the lie, yes lie, otherwise over and over again doesn't make the lie true.
Then there's the logical argument. Article One of the Constitution includes among other things:
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
The Constitution already gave the government power to arm its own troops, including the militia. The idea that we'd need an item in the Bill of Rights to give them the same power they already have is simply preposterous. Nobody with any intelligence and knowledge of the actual Constitution would think it were necessary. And the folk who wrote the Bill of Rights were certainly people of intelligence and very much did know the Constitution.
Today, the only question is, are the people who make such claims stupid enough to believe it, or are they lying and think we're stupid enough to believe them?
Without question, and from its inception, the Second Amendment confirms an individual right to keep and bear arms.