I doubt that you or your ancestors had a lawful claim to any property in DC, as the Bundy family did in Navada since 1877.
whether or not they have a lawful claim to the property, they have a grazing easement - which is more important than the property itself. Because, regardless of who owns the land, the owner of the grazing easement controls everything on the surface of that land.
But, aside from that small nit, your point is well taken.