When, as with the New Deal, a group of individual persons seizes control of the mechanisms of the state, the distinction is irrelevant. FDR and his cronies accomplished a successful revolution and ended up as the government. Beyond that, I don't understand your point.
The point is in the proper use of words. Words mean something. There is a big difference between possessing and exercising RIGHTS and possessing and exercising POWER.
He said that "persons" had the right. He didn't say anything about reptiles.
Although I’ll grant you, FDR was definitely revolting.