This is an interesting concept, and my disclaimer is that I did not read the old posts and did a quick read on the new ones.
My background is semi pro motorcycle racer, and counter steering a bike around turns comes so natural to me that I instinctively do it on my bicycle too, but only at high speed turns.
Some facts, from my experience: a slow turn needs the bars turned in the direction of the turn. On an average speed turn, you can simply just lean the bike over and never turn the bars but on questionable surfaces with grit, sand, gravel, etc you might need to slightly turn the bars in. On a fast sweeping turn at speed, counter steering (turning in the opposite direction of your turn by fractions of an inch at the bars) is an advanced technique to carry more speed through a turn, allowing later braking into the turn, higher speeds through the turn and ultimately, faster speeds exiting the turn.
Something to be aware of, while counter steering is an advanced technique, if done incorrectly, it could induce the rear wheel to excessively track outside the front wheel and cause you to slide out. Some might call this drifting and on two wheels, you'd better have more force pushing forward than you will encounter sideways. A trick is to exaggerate your weight on the outside pedal, more weight for more speed and tighter turns.
When done correctly, it will appear to someone behind you that you are drifting slightly. A word of caution, advanced tire wear, esp cupping of the front tire.