The TV's 3D conversion is not dependent on the source of the video feed. Running a multiplat on Xbox and on GameCube will give you the exact same 3D result. If they look like flat pieces of cardboard, then that is your TVs fault, not the system's.
However 2D to 3D conversion just really sucks. Just watch a few 3D youtube videos of dolphin on your TV and hopefully you'll be enlightened.
The PS2 & PSP don't have Z-Depth, and I don't think the Xbox original does, but I'm not sure about XBox.
Long story short, it is the Home Consoles & Handheld Console's fault for looking like flat pieces of cardboard.