Unfortunately there aren't many options to control what the user sees when they are already subscribed. ...okay for some pages but not so designer friendly.
When the "show groups" option is not checked I think it makes sense to hide the save subscriptions button as well. This has confused a lot of people using my client's site. Subscribers see a save subscriptions button right after they signup, but it's really not clear why they would need to click it. Groups are hidden at that point so it doesn't make sense.
Also... I understand them being able to unsubscribe but again, since there is no group list people are just seeing "unsubscribe".
I think to avoid confusion with these users that "hiding the groups" should take away the save button and change the unsubscribe message to "Unsubscribe From Newsletter" (but only for that widget's instance)
This is ideal for subscribe forms on the homepage. It looks pretty strange if you had a bunch of groups listed on a form on the homepage. and as you add more groups, it just breaks your layout.