The reason the gyroscope story got demoted is a lovely experiment. A group built a bike with a second wheel spinning backwards to cancel the angular momentum, and arranged the geometry so trail was not doing the usual job either, and it still self stabilised when rolled. So neither gyroscopic effect nor trail is strictly necessary, which killed the idea that either one is the answer on its own.
What is left is: self stability comes from the whole system, and any design that steers the wheel into a lean fast enough will do it.