I know this is old but still needs to be addressed. Invite only should allow them to see and post. If not invited then they should not be able to read or post by right.

Can we get this fixed or a hack or plugin written?

1.) In the (ACP) Admin Control Panel:
ACP --> Options --> Settings --> Group Options -> Allow Join-to-View Groups: Yes

2.) On the Groups page (Group Information) press: EDIT
In each invited group, the group manager must edit the "Group Information" and check the check-box "Users must join to view the content".

If your not viewing as an administrator or the owner of the Group, the results will adhere to the invited groups system.

If you wish to have further permissions. Assign a social group as a "secondary user-group" and alter the "user-group" settings in the User-group Manager accordingly.

Note - The group label will always be visable, just access to the group will be prohibited. To hide the group from showing, except to the groups members -- you will have to alter the template with a conditional and setup a secondary user-group for it.

My daughter has been using "social groups" for years. There is nothing wrong with the code that would require a fix, but the original documentation in this section could have been better and has led to some incorrect conclusions. :)