Not exactly correct.
Even Professor Amar was clear on this:
As scholars such as Stephen Halbrook, Michael Kent Curtis, Robert Cottrol, and Ray Diamond have documented in great detail, the framers of the Fourteenth Amendment strongly believed in an individual right to own and keep guns in one's home for self-protection. Most obviously, blacks and Unionists down South could not always count on the local police to keep white night-riders at bay. When guns were outlawed, only Klansmen would have guns. Thus, the Reconstruction Congress made quite clear that a right to keep a gun at home for self-protection was indeed a constitutional right--a true "privilege" or "immunity" of citizens.
Not quite clear enough, apparently. The U.S. Supreme Court, starting with The Slaughterhouse Cases, has listed the privileges and immunities of "citizens of the United States" and the right to keep and bear arms ain't one of them.
If an individual right to own and keep guns in one's home for self-protection is protected, it's protected by the state, not the federal government.