Explanation behind the pic is that my cat got on the ledge and immediately realised he couldn't balance properly because he didn't have the space to spread out because the bird was in the way.
I snapped the pic as he was using all his power and brain process to stay on the ledge - personally, I don't view the photo as my cat "Intensely looking" at the parrot. IMO he's not even looking at the parrot. I don't know what your experience is around cats, but that is not a cat with his attention caught, ready to pounce or swipe, - when cats intensely look at something, they are focused, faced on, and following the thing with their eyes. In that photo, that is a cat that realises he has made a mistake, and is looking for a way out. Seconds later he turned wobbly around and stood on the light you can see behind him (and broke it

) and if he hadn't, there was NO way I was going to leave him up there with the parrot because of the reasons you stated. This whole scene literally played out over about five seconds. I know that they can't be fully trusted - i am not delusional.
As wolf said: "need to be around our birds enough to be familiar enough with them to be bored with them and to find them generally uninteresting."
I think you misunderstand me when i say I let the parrot and cats in together. I DON"T DO THIS OFTEN, nor do I often let them get this close to each other - usually Julain will sit with me, and the cats will be snoozing on the end of the bed. I don't have them out often together like this anyway, just often enough so the cats don't find him interesting enough to want to "play" or "hunt" with.
I don't want to fight about this - we each have our own opinions. And that is okay - but like i said before, I feel it's safest to have a little interaction now to save a malling in the future if i kept them separated and then somehow they managed to get out together. They cats wouldn't be "Bord" or "Desentized" to him, as they are today, and that would be his death right then and there.