He's got it all wrong, it's ghosts.

I wonder if it has anything to do with why train wheels stay on the rails due to being tapered, and the flange is only there for emergencies. They're self-centering.

Like, when the bike wheel turns, it becomes effectively a larger system that wants to return to being smaller.

I had a similar thought, followed by an equally small desire to figure it out.

Both mechanisms involve wheels, but beyond that there's no similarity. The bike would still stay upright if the tyres had no width at the point of contact with the ground, so there was no increase nor decrease in the diameter of the wheel as the bike leaned.

It's weird how he locks the front wheel in place and says "so angular momentum isn't the cause", then goes on to explain that angular momentum helps to prevent the front wheel turning too sharply and so is actually critical in keeping the bike upright.

I bet you're remembering the clip of Richard Feynman explaining that function here on the sift?
http://videosift.com/video/How-a-Train-Stays-on-a-Track-not-as-simple-as-you-thought

I remember being fascinated by that. I don't think it has anything to do with this function in bicycles, but on the other hand I had no idea that was how trains stayed centered over the tracks either...