You can't turn a bicycle or motorbike without counter-steering, so these people are just not turning their bikes? It's not possible to not countersteer as the bike would lean to the wrong direction and you'd turn the wrong way (since you'd have been initiating a countersteer, afterall). Are you seeing people just manhandle the bars the wrong way in emergencies? I could believe that.
That's exactly it. Countersteering is a learned behavior that people aren't aware they do. They will describe it as leaning into the turn or whatever. Then, when they are in an emergency and need a tighter turning radius, they instinctively put in the wrong input and the bike straightens up. Explicitly teaching countersteering helps teach them to respond to emergencies with the correct input.
https://www.youtube.com/watch?v=9cNmUNHSBac