Problem with Airplay streaming from iPhone's TV app to Apple TV

I have a few iTunes purchased and downloaded movies on my iPhone's TV app. I can play them fine right on my iPhone. When I try to stream any of them to my Apple TV via AirPlay I get error 12162. The movie just wont start playing. Streaming via AirPlay from other apps like Youtube go just fine without any issues so I think there is a specific issue with iTunes downloaded content. I have checked similar issues and need to say that I have done all of the following and it did not help:

1. Check AirPlay is turned on on the Apple TV (turn it off and on if it already is)
2. Check that both devices are on the same network (Settings > Wifi, on the mobile device and Settings > General > Network, on the Apple TV).
3. Restart the Apple TV (Settings > General > Restart).
4. Restart the Apple TV by removing ALL the cables for 30 seconds.
5. Restart your router. (Also try removing it’s power cord for at least 30 seconds)
6. Restart your mobile device.

Error 12162 and no go.