Sorry, but characterizing Freedom to Roam as allowing people “camping in my backyard” is indeed FUD. Words like “my backyard” have a reasonable definition, and you can’t just redefine them at will (i.e. redefine “my backyard” to mean “my whole property”) to make the statement technically true.
As an American, yes backyard can mean the general area where one stays, but in the specific comment above, I also took it to mean literally in someone's backyard.