"Most people have seen a gyroscope in action, so the stability of a rapidly rotating wheel should be fairly intuitive, making this a focus from the start. People have built bicycles with counter-rotating wheels and found that they still remain upright, so that can't be all of the story."

Um, counter-rotating wheels are still gyroscopes. In fact they're extremely stable gyroscopes in that they won't impart rotational velocity on the frame. So by having the wheels on a bike rotate oppositely, you're actually making the gyroscopic effect even stronger.

I think Ars is pulling from this article, which isn't about staying upright but is about the self-correcting steering of a bike wheel (i.e. the fact that you can ride hands-free.) http://www.sciencemag.org/content/332/6027/339.abstract -- in which case the conclusion is correct and likely due to the geometry of the wheel. For example tractors have convex pulley systems that allow leather belts to self-center despite not being perfectly aligned. It's counterintuitive but it works.