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.