When approving the Bill of Rights, each former colony considered itself to be a free State, where State is synonymous with Nation. While the former colonies recognized the importance of working together, there was limited trust in the other States. Each State had its own Militia. Formal recognition that the central government was not to interfere with any State’s Militia was added to the Constitution as the Second Amendment.
This is not a radical reinterpretation of the Second Amendment. This interpretation is acknowledged by the current Supreme Court, in District of Columbia v. Heller (http://www.supremecourt.gov/...), specifically pages 3 and 25.