Well this is interesting (if you can stay awake thu the video). We kind of always thought it was the gyroscopic motion of the wheels that kept a bike in balance too, but maybe there's more to it...
Actually, we're reminded that in order to dive quickly into a corner while cycling you're supposed to counter steer (in the direction opposite to where you actually want to turn) in order to shorten the wheel base of the bike and allow it to tip over. This video seems to be getting at the opposite effect of naturally steering into the direction of the turn and as a result keeping the bike upright. It's interesting to see it happen all on its own though.