Thinking or instinct.....
During my investigation of many motorcycle crashes, the part of countersteering that I've noticed is that if you don't CONSCIOUSLY think about how to turn, in an emergency situation, your reactive brain will tell your muscles to do something to avoid death or injury. What it will tell most people is to steer the front wheel the way you want to go. Fully 75% of the crashes I've looked at where "lost control / went wide" resulted from the rider causing the bike to go the wrong direction while trying to turn or swerve which resulted in the crash.
The biggest issue with just 'riding like you know how' without the brain training (you training your own brain) is it usually results in causing the crash which is trying to be avoided. I've even investigated crashes where the bikes skid marks (braking errors too) went from their proper lane into the oncoming lane simply because they tried to steer when they swerved. Not stupid, but very ignorant of how the brain works under stress.
"Though no one can go back and make a brand new start, anyone can start from now and make a brand new ending." -Carl Bard