"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." Even if we were to change this to read:
"Guns are bad, they kill people, the right of the people to keep and bear arms, shall not be infringed." has exactly the same meaning when it comes to our rights. The first part of the phrase in no way modifies the second part.
Seems to me that the second amendment is stating, "The right of the people of a state to keep and bear arms shall not be infringed by Congress, since the people form the state militia, and a well regulated militia is necessary to the security of a free state."
To me, that's very different from your, "The right of the people to keep and bear arms shall not be infringed."