Yet another great question by an HD Beat reader. This really drove me nuts until I researched it. You sort of already know the answer, the picture is displayed in the appropriate aspect ratio regardless of the actual resolution. The reason is that not all pixels are square. Any image can be made up of any number or shape of pixels. When we watch 640x480 on a 4x3 TV the pixels are square as they are with 1280x720 on an HDTV. When we watch most SD widescreen video like Fox Widescreen or video games which are only capable of displaying a certain number of pixels, they use square pixels so they can produce a 16x9 image.
DVD players do this as well as video game consoles and cable boxes. This is why they all these devices have settings which allow you to set the aspect ratio of your TV. If you turn it to widescreen even though you don't have a widescreen TV the image will be distorted. Some cable boxes will actually add black bars on either side so that the image is not distorted by the TV. The interesting thing is that DVDs are 720x480 which also isn't 16x9, but thanks to anamorphic abilities of your player, your TV scales the image to the native resolution of your TV. All the more reason to go HD on your DVD player.
Fox Widescreen has worked like this for years, Fox was the first to update their infrastructure to digital, but before HD was prevalent, as a result they were reluctant to go HD and ended up the last of the 4 major networks to go HD. They were able to do this because their video was recorded with cameras with 16x9 modes that effectively shrinks the pixels to SD and then stretched them back at the other end. Fox Widescreen still continues to fool many people during promos and shows like Cops; people think they are HD just because they are widescreen. Some people have actually captured images of Fox widescreen in a 4:3 fame due to technical difficulties.
DIRECTV is also known to shave some pixels off in order to save bandwidth. Some call it HD lite, but basically instead of sending out 1920x1080 they will transmit 1280x1080. This is how their HD has some of the lowest bit rates in the business. But regardless of how many pixels they shave off we still see a 16x9 image.