Interestingly I have always intuitively counter steered on a bike (pushbikes as well at speed), even well before I first heard the term 'counter steering'. It has always seemed natural to let the bike tell me what it wanted to do and follow it's instructions as it were. Going around corners it always felt like the bike wanted to turn better with a bit of pressure on the inside bar so that's what I did, I didn't know it was counter steering I just knew it felt better.
It seems of late the term 'counter steering' seems to have acquired some magical, mystical meaning and everyone is suddenly concerned about it and making sure they're aware that they do it, but it's my belief the majority of riders who ride regularly will have been doing it subconciously for years and have only thought about it since it has become a popular topic.
I really don't get too concerned about the physics of it all, as long as it works and the bike turns when I want it to and I enjoy the ride.