Problems with OG private groups
There are two different fields:


Group visibility. It only exists for Groups. It controls whether all group content is visible to non-members by default.
Group content access. It only exists for Group content. It controls whether a particular node in the group is visible or invisible to non-members, or whether it should leave that decision to the default setting of the group.


Check whether your group has a group visibility field and whether you have the permissions to edit it, and if not, add that field via /admin/config/group/fields and grant the right permissions to edit it.