The case I describe is that you can only setup one category in the XFMG for Social Groups. It can be "hidden" from the XFMG categories navigation
but when a user has the full path to that category he can see
ALL media from
ALL groups, no matter if he is in a group or not...
For example, I assigned a XFMG category named "social groups media private" to Nobita Social Groups and if I put the URL into the browser, every registered user can see all media from all groups...
https://www.mywebsite.com/media/categories/social-groups-media-private.34/