If, under this rumored Apple cloud-based service, users would still only have access to their own library, I don't see why the record labels are pitching a fit. So the music is streamed off of Apple servers rather than your home computer. You still only have access to the songs in your library. All that would change is the need for users to manually sync devices. What's the big deal?
One situation is where the owner of a copy of the work accesses the very same copy he owns.
The other situation is where someone who does not own a copy of the work transmits a performance of the work.
The second situation is like someone who owns the song calling the DJ to make a request - the radio station needs the proper license, regardless of who made the request.