So far, there is no evidence that being a member of our group, even if made a member against your will, shows up on your facebook page to a non-member - which is surely the whole issue.
I belong to a closed group on FB. On the group's FB front page, all the members of that group are on display to non-members including me and my pic. None of the content or discussions is displayed - you have to be a member to view them. But, depending on the group's privacy settings (I'm assuming), it is possible for anybody on FB to see who has joined the group.