If your bike is badly set up, for example the seat is way too low, and you are using too high a gear, I suppose it's possible that your efforts would be so inefficient that you would cycle more effectively standing up, but otherwise seated is more efficient.
The problem with his gravity explanation is that while you use gravity to push down the pedal, at the same time you have to resist the effect of gravity pulling you down too. When you're seated, the bike supports part of your weight, while when you're standing, your leg muscles have to hold you up.