I appreciate the opportunity to express a wider view of "steer right to turn left" without this turning into an inferno.
I agree 100% that a typical street bike will not turn without "counter steering". That does not mean that every motorcycle works that way at every speed.
A trials bike is pretty much the other end of the spectrum from a street bike. I probably only have a couple hundred play hours on a trials bike. Anyone that has ever ridden one knows that you can see the front of the front tire pointing left in a left turn.
I know when I turn off a berm early on a mx track I turn the bars (front tire) left to turn left.