True, although the video output could be setup in one of two ways, and I have a fealing it's probably the second. The first way it could be done is the Xbox console divides the video up into the number of players and then transmits it to the correct controller. Or two, the Xbox console sends the video signal for all four and the Xbox controller determines which one it's responsible for. The reason that I would say it's two is that there'd be no way for the Xbox console to divert the right video to the correct controller easily, and it would make for a more complex video setup. Wheras it's extremely simple for each controller to know which player it is and filter out the rest of the signal. When I refer to controller here I'm talking about the light gun. The only thing is whether the data on the yellow wire is in fact a composite signal in its entirety or a stripped down proprietary version with only the neccesary coordinate data. See, the guns work by having the Xbox insert coordinate signals on every other scan line on the TV and then having the gun detect these coordinate signals and compare them to a matrix to know where the user's pointing. Therefore the yellow wire could either carry the entire video signal, coordinates and all, or just the coordinate signals. If it just carries only the coordinate signals a display in the controller won't work since the video isn't there. Yet another setup would have the controller send the coordinate signals it receives from its sensor in the reverse direction back to the Xbox console, which would also prohibit a controller screen. Now that I say that I'd most likely say it works using this new method three, having the light guns receive the signals and transmit them back to the Xbox, which as I mentioned before would be useless in trying to connect a screen.
Now to explain to other people who don't understand why this doesn't work and HD and projector: It probably doesn't work on HD because the Xbox wouldn't insert data on every other scan line beacuase this would reduce the quality of th video output to that of composite video and defeat the purpose of HD, therefore it would be pointless for M$ to waste time implementing it since every Xbox comes with a composite AV cable anyways. And the reason it doesn't work well on projectors is because the signal probably isn't accurate due to lower quality inherent of projectors or completely intact since its converted to light rays shooting out into an uncontrolld environment and then bouncing back again through an uncrontrolled environment. Whereas in tubes and projection TVs (not to be confused with projectors) the light hits the phosphorous of the TV screen in a controlled environment with high quality and then spends a short time out in the open.