The people promoting this theory are engaging in classic conspiracy-theorist thinking. They're latching on to very small details, to ambiguities, and relentlessly interpeting them in the worst possible light.

There's not one of the items of "evidence" here that doesn't have multiple possible explanations.

The lawn chair? Geez, that's a generic design used around the world. I have a couple in my back yard, and I don't live at Abu Ghraib.

The wall color? It seems to be popular in Iraq. Earth tones in a desert country are hardly unusual. We didn't build Abu Ghraib, so it would only be remarkable if it didn't share architectural features with other facilities in Iraq.

The prison uniform? Not only don't US forces have a monopoly on them, do you think it's possible they were used in Iraq before we invaded? Dayglo orange is an international standard, because it makes escaping prisoners easy to spot and shoot.

Here's the interesting thing: You can add up all those details and make them meaningful in exactly the opposite way. Do you suppose that maybe whoever made the video deliberately used those props to send an unmistakable message that the execution was explicitly about Abu Ghraib? Especially the prison uniform--"you mistreat us when we're your prisoners, we execute you when you're our prisoners".

I don't have any proof of the latter theory, any more than you have proof of the conspiracy theory. These things always peter out into a fog of ambiguity. Fertile ground for tabloids, a swamp for people who think.