I think their meaning was something closer to your last paragraph - there was nothing interesting there before so it didn't matter that there was no public right of way.
But now there are things on private land that they are interested in. If you're thrown off a private road on your way to a pizza restaurant that's on it, you wouldn't have the same rights you're talking about for owners (or leaseholders) of properties on the private estate.
But now there are things on private land that they are interested in. If you're thrown off a private road on your way to a pizza restaurant that's on it, you wouldn't have the same rights you're talking about for owners (or leaseholders) of properties on the private estate.