OK, silly question maybe, are you sure you are not looking at the bezel as the black area? That monitor does have the resolution you are using, and if Windows is setup for that, I don't see why it would not fill the entire screen.
The display should have come with a disk that would have some setup files. See if installing them will help, maybe update the drivers on the video card also. I don't see a driver download for the monitor, but maybe the color and size profile is on a CD in the packaging. It's usually a .ini and I think a .inf or .ing or something. Don't remember what the color profile files are called.
I did some poking around I think perhaps that this is more video card related.
I was checking out settings in the ATI CCC and I noticed a scaling alteration there. By toggling the setting I was able to fill the screen.
The question though now becomes why do I need to do that when both the LCD and GPU support 1920x1080.
I am sure there is some sort of setting I am missing but I am not sure where to start in the troubleshooting.
What you are seeing is a common issue with ATI's Catalyst and HDTVs. I agree that it makes no sense and is a pain.
The issue is probably related to how different HDTV manufacturers implement resolutions standards differently. Whereas, monitors have the ability to report settings to your GPU automatically (HDTVs can, but it is different) and standards are more widely implemented in a common fashion.