Spoiler alert: they didn’t create a corporation.

They incorporated Washington DC so that it could have its own city government. Previously Congress was solely reliable for the administration of DC. They passed off that responsibility to a separate city government so that they could do other things like impose taxes, establish central banks, start wars under false pretenses, and in general screw you over.

Then later some gullible and ignorant people read the act, saw the word “incorporated” or “corporation”, and assumed that the act was talking about an economic corporation. They didn’t bother double checking, and instead ran wild with theories based on a false premise.