"I wonder if in the past someone official or otherwise dug in these three places looking for evidence of the 'missing' stones that would have made up the circle, then just back-filled them afterwards and that's what they've 'discovered'?"

Yes. This could be a significant problem. In addition, were you to construct such a circle, it would make sense to spend a day or two checking all potential hole positions (by digging them out) even if you did not intend to use all of them. You would probably want to do this before you send a few hundred people off to spend the next few years hauling stones 20 miles to the site: They will be mighty miffed if some of the stones turn out to be the wrong length.