This might be the primary source:
http://www.bloomberg.com/news/articl...eaming-devices
But is it Apple's fault that Amazon does not have an app for Apple TV? or is it Google's fault that Amazon doesn't publish Amazon Video to Google Play (with Chromecast support)? Perhaps, but I've never heard Amazon claim that to be the case.
For sure, there would be no Buy button in Amazon Video for Apple TV, but on what basis would Apple reject such an app otherwise? Similarly, while there is an Amazon Video app for Android, it seems it was Amazon's choice to deliver it via the goofy means of side loading Amazon store app. Google does not take a cut of digital sales unless you want to use their ecommerce system (i.e. purchase with Google Play account).