When watching a streaming video on the Wii's Nintendo Channel, you can clear the white bands across the top and bottom by simply pointing the Wii-mote away from the TV.
Since your typical action when using the Wii is to keep the controller pointed at the screen, you might have wondered if there was a way to make the video more watchable rather than matting over the standard definition 4x3 aspect ratio.
As best we can read Nintendo's UI design team, pointing at the screen signals your desire to interact with the video (you can click Back, Pause or Details) while setting the remote down or pointing it away makes you a passive watcher who gets to enjoy it full screen. Maybe if the videos were longer and not mostly short marketing clips, we would find this more intuitive and would have discovered it sooner...
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Or they could have just told us... hmmmm what a concept.
In Nintendo's defense, I thought it was intuitive enough and got the thing to go away after a few seconds of watching my first video a while back. Moving the Wiimote pointer off to the side was probably the first thing I tried due to online video sites (and computer DVD programs) that respond that way when having the mouse over the playback screen.