Sandy – this will sound kludgey but here goes:
So you have user group A that should see the Title and the view, and user group B that should see nothing. If the Title that you want group A to see doesn't have to be the Title Bar per se, you could permanently hide the Title and Border, and use one of the quest menu webparts as a "title" above the qListView. Those webparts can be hidden by group as well.
The Quest Menu webpart wouldn't have anything behind it – it wouldn't have to be a working hyperlink. And it could either have just one entry (which would be the title) or if you want to use the webpart's source list for other purposes, you can configure the webpart so that it only picks up the one item that is functioning as the title.
Does that make sense?