re: “You are very correct that its unlikely the(y) damaged anything.”
No, you are both very wrong about that. This isn’t just a simple case of government bureaucracies; there are valid archaeological factors of concern.
The sand on the high plains is a light-colored, fine-textured variety. However, because there isn’t a lot of wind there, and almost no rain, the surface layer of it remains relatively undisturbed over hundreds and thousands of years. That allows that surface layer to oxidize and form a thin, darker crust over the lighter sand beneath.
The natives who made the designs did so by breaking though that crust and exposing the lighter sand beneath to make the patterns visible from above. Those breaks have remained for centuries, and for the same reason so will the footprints of the Greenpeace vandals tracked through the area, like more or less permanent graffiti. That is the damage.
Well, then, they should be able to post evidence of the damage actually done.