Hiding group_group field programmatically
You should be able to hide the group_group field with the $form['group_group']['#access'] = FALSE; this is used by the Hide checkbox on the field settings page and this is how it works.

However, if you testing as an anonymous user maybe you have this issue: https://www.drupal.org/project/og/issues/2278003 there's a patch which fixes the access itself.