The theory goes that Apple's ulterior motive could be to control the media you consume via digital rights management schemes, intentionally restricting the use of copyrighted music and material to proprietary hardware. As Nilay Patel of The Verge points out, Apple Music is a streaming service already rife with DRM restrictions. It would be fairly easy to extend those restrictions in such a way that users would only be allowed to stream music via Apple-approved speakers, headphones, and devices.
Rights-obsessed record companies would also get their kicks in this dystopian scenario. Catering to the demands of record execs, Apple could prevent you from listening to any album or song, or watching any video, that you didn't legally obtain, or download from a preferred source. Of course, Apple calls this a "pure paranoid conspiracy theory," but that doesn't change the fact that it could do this if it wanted to.