My understanding is that Apple is not blocking Amazon Video on the Apple TV. It is Amazon who refuses to put it there. They even removed the Apple TV from Amazon.
One other thing I might mention. Although HDMI cabling is digital, it turns out that you can have HDCP problems if you have cheap cables. Out of the blue I started having problems with DirecTV (black screen) and my Roku Stick (gave me a copy protection error with Amazon Video). My signal paths were DirecTV > Oppo 105D > Yamaha RX-A3000 > Panasonic TC-P60ST60 (I'm waiting until OLED prices drop) and Roku Stick > Oppo 105D > Yamaha RX-A3000 > Panasonic.
For years I have though how ridiculous it was for people to spend $500 or even more for an HDMI cable. It's digital, right, with error correction. But then I read:
http://www.soundandvision.com/content/uhd-blu-ray-vs-hdmi-let-battle-begin#0cfzlwjKyZfPjpsV.97
where a number of brand name cables (Monoprice, Monster) failed to deliver 4K video.
Turns out that there is no error correction for HDMI video so cabling can be important, depending upon your installation. As I will eventually be going to 4K I contacted Audioquest regarding their Carbon cables which did the best in the tests. They told me that their cables were in the process of being 4K certified up to lengths of 15 meters only.
I found on e*Bay a 9 foot Audioquest Carbon cable for about half price and took the risk that it was genuine. (You can send in a cable to Audioquest to have them verify that it is genuine, but they will destroy it and not return it if it is not). Replacing the cable between the TV and my receiver made the problems go away.
This is not likely to be a problem in your installation, particularly if you purchase from a store and have them install it so it is their responsibility to make it work.