Amazon are not going to put content on a provider's box until they abandon FireTV?
... Maybe, but Amazon's model hasn't hitherto been about hardware really has it? Witness Prime Instant Video app on iPads. Prime is a wide offering, video being just one part of it and not having to have yet another box coule make prime more appealing. I suspect there are plenty of people on Prime already without Fire TV. Having an app on other platforms, in that scenario, makes sense.
The sticking point, no doubt, is in app purchases. I can't see Amazon ever giving up on their own billing relationship and paying Apple a cut of any rental or sale outside of Prime video.