When you try to JA into a members only group you, as expected, get an error.
However if you then want to post it somewhere else - perhaps you spent 5 mins writing an awesome cover note, you need to click the minute 'x' next to the group name. This isn't that intuitive or discoverable IMO.
Two suggestions therefore:
1. Allow clicking anywhere on the group name field to let you select another group.
2. and, perhaps not allowed by the core? allow an attempt to post to a members only group to constitute a combo 'join the group' and post content.