I've seen the same claim from a lot of people who seemed to have thought about it a lot: that you always countersteer on a two-wheeled vehicle, but you only do so consciously if you're riding a very fast vehicle or you want to turn extremely quickly. (A deliberate countersteer is taught in some bicycle safety classes as an "emergency quick turn".)

This is counterintuitive to me as a regular cyclist, but I realize that most of my cycling skills are completely unconscious, so I don't have a lot of confidence in my ability to describe exactly what I'm doing on my bike.