I've had this (fairly consistently) - both with music and movies purchased on the iPhone, not purchased through iTunes.
In some cases, I noticed that this was the result of an interrupted download - be it a network interruption or an inactive screen - and cancelling the current download and starting a new one. Granted this might not be the explanation for all instances of this, but for my most noticeable "Streams", this was the case.
I'm currently experiencing this with Furious 8 - redownloading to completion using the phone will fill that entry in when using iTunes to view the device contents. However, once the file is deleted (either removing the download through TV, removing through Settings, or removing through the same iTunes display) and a sync/backup is performed, the same "Stream" ghost entry reappears.
Outside of an erase and install, the only way I've found to remove these entries is to use something like iExplorer to access available parts of the iOS file system and delete the actual "Purchases" folder from the device. Should you choose this route, make sure you transfer any available purchases first from the iPhone that aren't already in your iTunes library - regardless of the media type (Music, Movies, TV Shows), it appears that iOS stores purchased media (from iTunes) in a different location on the device compared to transferred media. Deleting the Purchased folder will subsequently remove the media from the device, and will have to be added back manually afterwards.
Note: The folder does get recreated in the file system upon the next purchase using the device.
Double Note: Leave the "Downloads" folder on the device alone. I've deleted this one mistakenly, and resulted in no download from any app (iTunes Store, Podcasts, etc.) being able to start. (probably because the expected target folder is missing) A restore is the only cure for this one.
Re-syncing after the Purchased folder is removed *should* get rid of the stale "Stream" entries at that point. It could be some junk data in one of the SQL tables causing this, but haven't been able to prove this for certain.
Steve
(good to see you're still around... you answered some of my questions ages ago - hope I can return the favor finally)
