On Windows it works fine with this setup, so it's an Ubuntu issue. I am running HDCP capable HDMI cables to an HDCP capable TV as a dual monitor from an HDCP capable graphics card.
The protected content would not be streamed over unprotected media. High-Bandwidth Digital Content Protection usually authenticated all devices in chain. So that include application->Display Driver->Graphics Card-> Serializer(on host side) -> deserializer(on display device side) -> Display Device. HDCP usually encrypt data when transferred over cables(HDMI etc). But software that renders data can request underlying device content protection status. So things can go wrong at lots of places.
Problem is most likely with driver of your display adapter/associate serializer. You can try to get latest graphics driver for display adapter and display monitor. Also how are playing video via desktop app or web browser?
Hope this helps
Stay tuned, I'm pretty sure the day HDCP get the whole stack from kernel through DRM (as in Direct Rendering Manager) to userspace up and running you'll see a big article on Phoronix. It's a slow work because of other things in priority, and because any kind of DRM (as in Digital Rights Management) have always been a subject of hot controversy.
The only way to get Amazon HD video streamed was through the flash stream through Firefox using the HAL PPA this is the link to that:
I'm not sure if it still works because I don't use flash anymore
The html5 stream works but HD is not supported at this time. Although tv shows do come through in HD. Just not movies. Since I run linux exclusively the best solution for me: Buy a roku. A roku 2 is about 35 bucks on amazon and it will stream anything amazon, netflix, hbo, etc. If you need a QHD or UHD get roku premiere.