You are the only one trying to draw that distinction. Everyone else just reads it as "the right of the people to keep and bear arms shall not be infringed"... regardless of whatever organized/unorganized status they may be in.
Well, there's your problem. Everyone I know reads it as, "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."
(Hint: That's where people get the "well regulated" from.)