I'd recommend just googling how a bike works instead of pursuing this argument. There's lots of good articles, like this one: http://www.cyclelicio.us/2011/bicycle-dynamics/ It looks like my theory on wheel angle may not be entirely true either. You can also find videos on youtube.

The Veritasium video is the best one I've seen but he only describes how counter steering works at slow speeds which is more like how you balance a stationary bike. The faster you go, and the bigger the wheel, the more the counter steering is done by gyroscopic motion than moving the wheel back and forth beneath you.

You could disprove that by letting a bike, without rider, roll down a slope.

If it rolls oriented forwards it will stay upright by itself because of the steering.

If it rolls oriented backwards it falls over because the steering now pushes it off balance.

If the gyroscopic force was the most important thing keeping it upright it wouldn't matter which orientation you let it roll.