To anyone with this problem:
Explanation: you have a song that was purchased with that unknown email address and you somehow obtained it and just can't remember when or how. But you say you don't even have any songs in the Music app. Well, iCloud restored all your apps, and it's also STILL trying to restore all the music from before. Until you enter the password for that unknown email address, it will keep bugging you with the annoying pop-up. Now what?
Solution: ignore the pending iCloud restore for now. Connect your iPhone to iTunes and sync all your music that way. Basically, you're helping iCloud to complete the restore process by syncing all the music yourself, thus not needing to enter the password for that unknown email address.
More in-depth: when you restore stuff via iCloud, you HAVE to enter password for each different account instance. When you restore via iTunes, you DO NOT have to enter password for anything. That's exactly why I back up to iTunes, restore via iTunes, and just deal with iTunes altogether. iCloud is not 100% flawless yet.
Hope this resolves any unresolved issues.