LCD setup and DVD setup are two different menu systems. When I told the DVD that it was outputting to a 16:9 screen, then set the LCD to 16:9, I get full scope with correct letterboxing.
It hadn't occurred to me that the cheapest way to integrate a DVD player into the TV was to just stuff one into the case, connect two sets of wires to the infrared pickup, and use a multi-function remote. But that seems to be exactly what they did.