This video also shows without highlighting the bad side of this type of differential... When you get stuck, its always the wheel with no traction that spins! DOH!
Actually, i think it was showing a '1 wheel drive' car getting stuck. I could be wrong, but i'm too lazy to go back and look 
The above person is right and so are you. A one-wheel-drive car has the dis-advantage that if the drive wheel has no traction, then the car does not move. ALSO in the case of a PASSIVE (IE the one in the vid) differential the wheel that is more apt to move may (in the case of ice or slick mud) be the only wheel to move. So for the type of differential that they showed; if one wheel was on ice and one wheel was on tarmac then the wheel on ice would spin but the one on tarmac would not (for non-UK/Eire's that would be pavement) spin.
It basically breaks down to this: With the type of differential they show in the video (which is still the most common type) you will only have as much traction as the tyre(tire) that has the least grip.
Here in the US, us motorheads (in the UK/Eire also known as people who have too much money to spend on a project car) tend for positrak or a differential that can be LOCKED. ( Too bad I sold my Ford Prefect Ranger 4WD. It was the REAL kind of 4WD, with locking hubs, and a true locked differential (4WD Low))
Never again will I get a truck like that for 400 bucks... :<