That theory and gold fringe flag are baseless wastes of time.
All cities are incorporated as the means of establishing a local government with the consent of the governed, i.e., a vote of the people. Anyone saying that 1871 law changed anything about the republic, except by establishing a new city government for DC, is pushing garbage.
The gold fringe flag has no meaning in the US except for use ceremoniously and typically indoors and at the discretion of the folks setting up the display. In fact, the code is considered to allow the fringe for ceremony as opposed to defacing the flag. It's a decoration on the flag that is permitted by code, although not explicitly, and has no military or legal meaning.
You're right anon, stay away from those garbage theories.