If you're talking about PC games, there are sometimes options to pull the HUD in.
If you're talking about console games, none really push the HUD out past the overscan area... console games account for overscan.
You can adjust this in the service menu as I said before. It's just if you cut it really close, you'll see the edge of the image sometimes. On top of that, it looks really bad because it accentuates any problems in geometry since you won't see a perfectly edged rectangle, but it will probably look wavy on the sides.
Just overscan it a little. Enough so you never see the edges of the image. This is best done on a PC, find an overscan pattern or something (I'd email you all my tools, but again, no computer right now), and set it to like 50 pixels on the sides, then instead of overscanning the top and bottom, just adjust the height until circles are circular and the top/bottom overscan will then be set.
Yes, a fixed pixel display would be the only way to get a zero overscan image. It's hardly worth it, especially just to eliminate overscan. Even plasma TVs and the such ship with an overscanned image... you'd have to enter the service menu on those to fix that. Overscan is just a necessary evil in the world of TVs.