I think you're thinking of it backwards. Amazon Prime video working on iOS and AppleTV is in Apple's interest because it means however many prime members will

I think you're thinking of it backwards. Amazon Prime video working on iOS and AppleTV is in Apple's interest because it means however many prime members will use those devices. Apple's content strategy is purely about selling hardware. Apple's not getting into the content business like Amazon and Netflix are (both of them are producing original programming... all Apple's done in that regard is the iTunes music festival in London which seems to be more PR event and technology test than anything else.) This is why Apple worked with Netflix, HBO, etc to get apps on the Apple TV even before the TVOS was ready.