This was not a personal privacy concern per se, but consideration for the protection of a sacred site. When @watmildon and I were working on the Sq___ renaming, we decided to remove the node for the Stone Mother from the map. The site is a sacred place for the Paiute people and had been subject to vandalism. Online resources from the Paiute people were careful not to disclose the location of the site and discouraged people from finding it or visiting it. There is no longer any public access to the site, so the reasons not to map it seemed to far outweigh any justification for mapping it.
I believe the GNIS record for this feature still exists but has been hidden so that the location is not publicly disclosed.