I'm running full screen on a 55" TV at 1920 x 1080. Looks pretty sweet, I must say. I've been using my TV as a monitor for the past 5 years, and I've never seen a game do the 'monitor size' thing that you describe.
Yeah, the 'monitor size' thing have to do with the TV settings. I guess he have it set on "unscaled", "pixel by pixel" or whatever it might be called, so when the game runs in a lower resolution than 1920x1080, it remains unscaled and is displayed inside a black box.