Initial review of the District of Columbia Organic Act of 1871 seems like it only sets up a local government (like Chicago or Seattle); how do you get that they formed a private corporation?
If you take the Act out of its historical context and, from the present looking to the past, imagine who the parties involved are, we might agree. However, we cannot do that; to best understand what really happened we follow our:
Standard for Review Rule 1: To understand any relationship you must: 1. First understand who the parties are; a. Always know yourself first b. Discover the true nature of all other parties second 2. Then you must understand the environmental nature of the relationship; and, 3. Only then do the actual terms of the relationship begin to have meaning and bearing on the relationship. Rule 2: To have any hope of understanding any particular situation in any relationship you must have first applied Rule 1, only then do the details of the situation in question have any meaning; therefore, review such details in accord with Rule 1 as well.
Thus, to understand the parties involved in the District of Columbia Organic Act of 1871, we must first understand who the parties are involved in the relationship described by the Act. We are not here going to delve into the Act in its entirety, suffice it to say, looking over the situation we find the Act is one made by the original jurisdiction Congress, set by the Constitution for the United States of America. The District of Columbia Organic Act of 1871 describes its venue as: "all that part of the territory of the United States included within the limits of the District of Columbia".
The District of Columbia was originally provided for in the Constitution for the United States of America (9-17-1787) at Article 1 Section 8, specifically in the last two clauses. Then, on July 16, 1790, in accord with the provisions of those clauses, the Territory was formed in the District of Columbia Act, wherein the "ten mile square" territory was permanently created and made the permanent location of the country's government, that is to say, the "territory" includes the actual government.
Under the Act Congress also made the President the civic leader of the local government in all matters in said Territory. Then on February 27, 1801, under the second District of Columbia Act, two counties were formed and their respective officers and district judges were appointed. Further, the established town governments of Alexandria, Georgetown and Washington were recognized as constituted and placed under the laws of the District, its judges, etc. The United States Supreme Court has repeatedly called this act the "District of Columbia Organization Act" or the "Charter Act of the District of Columbia" and recognized it as the incorporation of the "municipality" known as the "District of Columbia".
Then on March 3, 1801 a Supplementary Act to that last Act, noted here, added the authority that the Marshals appointed by the respective District Court Judges collectively form a County Commission with the authority to appoint all officers as may be needed in similarity to the respective State officials in the states whence the counties Washington and Alexandria came, those being Maryland and Virginia, respectively.
According to the United States Supreme Court those charter acts (first acts) were the official incorporation of the formal government of the District of Columbia as chartered by Congress in accord with the Constitution's provision. Again, the Supreme Court called that body of government "a corporation", with the right to sue and be sued. Since 1801 The District of Columbia has been consistently recognized as a "municipal corporation" with its own government.
Congress wrote: That all that part of the territory of the United States included within the limits of the District of Columbia be, and the same is hereby, created into a government by the name of the District of Columbia, by which name it is hereby constituted a body corporate for municipal purposes ... and exercise all other powers of a municipal corporation