I don't think there will be a legitimate way to "fool" the system. In your audio example, your app is not remaining in the background pretending to look for an audio stream. It is telling Apple's audio process how to obtain the music stream. When the app is not in the foreground, it goes away completely. It is Apple's audio process that continues to stream the music.
The task completion suggestion is the only real possibility of maintaining a temporary connection for a limited amount of time after quitting the app.
This is completely wrong. Like, 180 degrees wrong.
ScaryRobot has posted what I believe is an accurate description of how background processing works a few posts up. I think there are few misstatements in my previous posts, which are, after all, just speculation based on the public presentation. If anything, my comments - although describing more flexibility than that of the naysayers here - in fact, portray a more restricted environment than actually exists.
I'm saying that I was probably wrong on some minor points, but I erred on the side of the nay-sayers. The reality seems to be even more liberal than I had thought.
It seems I was wrong about Local Notifications being a way to schedule call-backs to the app. Frankly, I've never used the current Notifications system and so was unfamiliar with it. Local Notifications appears to be simply a way to schedule a future notification to the user, who can then choose to switch-back to the app. Mea culpa. But it looks like if you have an audio, GPS, or VOIP app, you really do get true background processing. As ScaryRobot has pointed-out, these categories are arbitrary and artificial. If your app does these things, and does background processing, it will be approved for the App Store. If it doesn't, it won't.
Fortunately, my interest is in GPS apps. Specifically, GPS apps that would only be practical if running constantly as you move around, while allowing the user to work with other apps. Check.
Those who are interested in understanding background processing should read and re-read his post. Non-developers are reading between the lines in the presentation and seeing restrictions that aren't there. Developers (at least, experienced developers who have written code for background processing) no doubt have already read the documentation and are shaking their heads all in the same direction.