Push notifications would probably be able to handle that :0 sending the music data to the server while the app is not open, then stream/send the music to you like they send notifications to you, but this would mean that apple has to make the API for it to allow something other then information (text) and be allowed to have it stream without interuption. Like after you quit pandora it would say 'would you like to have the music stream to you using push' and you say yes and it turns on push and then blah blah blah it streams.
That's just silly.