Items are not required to be a member of a Group. But if you have a Group that has no members then that Group is not doing anything for you nor will that Group ever receive a command or update and therefore cannot be used to trigger a rule (which is how I read your original question/problem).
Groups are useful for far more than the UIs. In truth, their use in the UIs is probably their least useful uses. They can be used to:
- aggregate the state of several Items
- trigger a rule when any member of the Group receives an update
- send a command to all the members of the Group (e.g. put all your lights into a Lights group, put Lights on your sitemap as a Switch and if you toggle the switch all members of Lights will turn on/off)
- find an Item by name
- control how Items are persisted
- put more than one Item on a single chart