Just looked at your post of the re-erected stone in Mach. This might fit in with what Four Winds' reply, suggesting that a fake circle was erected for the 1981 Eisteddfod. It IS the Explorer map that a Standing Stone is marked on, so perhaps they (criminally) removed this stone and re-erected it at the site in the cul-de-sac and replaced it with the fake circle!
Beggars belief really!
The other possibility is that I may have read the map wrongly as I now notice a dot to the left of the words "Standing Stone" where I believe your stone is, as well as another dot to the right, on the outcrop, where I was looking!