My setup is PC => HDMI reciever => TV. As far I get it, if you have a receiver in the middle, you'll get a green screen on your TV. If your display is connected directly to PC, you will get a black screen. This might not be 100% true because I tested only with 1 monitor connected directly (and saw black screens).
I bought Powercolor 5600 XT 6 months ago and I was struggling with green screens all this time. Every day I saw at least one green screen crash, usually more. Crashes happened at random, GPU load was not a factor. Nothing was a factor. Funny fact - I never had a crash while running Furmark stress test. There was one distinct sympthom - if you launch a 3D game you might see artifacts, horizontal bars with corrupted image. If those appeared it would mean you will 100% get a green screen crash pretty soon.
I've tried everything except modifying GPU BIOS. Nothing helped. Finally I flashed an original 1st gen BIOS from Techpowerup and it solved the crashes. So in my case a 14 GHz BIOS was the root cause.