In the OG fields UI, the content group visibility field says:

" Determine access to the group content, which may override the group settings."

To me, this says: "Add this field if you want your group's content to be able to override group settings. If you always want your group content to inherit from the group settings, you don't need this".

This does not appear to be the case. Without this field on my group content node type, I can't get the nodes to be private even though the group is private.