I encountered the term "counter steering" a few years ago, after I had been riding for many years. Read an article about it, but didn't really get it. Subsequently realised that I had probably been doing it for years, and decided that "counter steering" was probably a term invented by some instructor to impress novices.
I use different cornering techniques on different surfaces and in different situations.
The only potentially serious accident I have had (35 years ago) was caused by a car passing another car at high speed, pulling in and sideswiping me. "I didn't even see you," said the driver.
He was at fault, but if I was more aware of what was going on around me, and better positioned I could have avoided it. An in depth knowledge of counter steering would not have helped in the slightest.
That incident made me aware of the need to use my ears as well as my eyes, to check mirrors frequently (and glance over my shoulder before changing lanes or turning at an intersection), and to be conscious of my position on the road.
Basic bike handling skills are important, but baffling novices with fancy stuff is counter productive. As important, if not more so, is road craft in traffic. Thinking ahead about where you want to go, and being aware of what is going on around you.
I read an interview with a bicycle courier in Bangkok yesterday. On avoiding accidents he said that he had learned to look at the faces of drivers to read what they are going to do.
"Hmmmm," I thought, "I can relate to that, and observing the position and behaviour of vehicles on the road."
At the same time be aware that anything can happen (and often does here in Phuket; even Bangkok traffic is more disciplined!).
Here in Phuket my daily ride is a bicycle; my motorcycle is for high days and holidays. The principles are the same.