A bug was reported where users can’t message groups unless they can also @mention them. pfaffman discovered this issue and explained that even though a user can type a group’s whole name to message it, the auto-complete list only recommends groups that can be @mentioned. sam confirmed this issue on meta, sharing a screenshot of the problem. The issue has been fixed by tgxworld with a commit to the Discourse repository.
It seems that in order to be able to message a group you must also have to be able to @mention it. If you cannot @mention a group it won’t be recommended in the auto-complete list of users; you can, however, type the group’s whole name and be able to message the group.
Now that @mention and message are separate settings, it seems like a bug that completion on the message interface works only if you can also @mention the group.