I do see your point, but it’s important to consider that the group security system is not specific to the @admins group. The same security model would need to work for the @super-secret-lurkers group, if a forum had one 
Being able to work out ‘not in a group’ is ultimately the same as being able to see ‘in a group’.
Yup, makes sense. Does updating the admins group to be visible to ‘everyone’ work for you?