Actually no. A rider can change direction mid corner (tighten a line) by adding more weight to the inside and add lean angle (which would mean there was a counter steering moment). However, a rider can also Add weight inside AND pull the inside bar and add steering. Both are effective and both have their uses. One adds lean angle, the other takes away lean angle. Both add steering. As we add lean angle we sacrifice grip and change the gearing of the bike a bit. There are times and place for either, I'd argue. Most riders have never experienced changing direction by only adding steering. The one thing I prefer to NOT do, is to add any bar input the opposite direction (with my palm say) of my intended travel. F-that...
Bikes change direction the same as a car, go cart or Can-Am (tm). The front tire must point in the intended direction of travel for the vehicle to set an arc. It's merely how we get to this arc that everyone seems to argue over.
I think I know what you are talking about because of an experience I had in my driving youth...
The wife used to work in South San Francisco in this huge industrial office park that had a very wide main road that looped all around the complex (It was wide for the large trucks that had to negotiate them) and ti was normally empty at the end of the day and the surface nearly perfect.
I used to get to her pickup point early so i could do "laps" in my car before she got there (lots of fun, no police)
There was this one corner that constantly gave me trouble and it was a sharpish, left hand sweeper slightly off camber, and it would always bug me because unless I tiptpoed around it (relatively speaking) I would spin the car as it unloaded the suspension in the off camber downhil crest.
One day when I was lapping happily, right before said corner, a rabbit ran across the road and I twitched the wheel trying to avoid hitting it, and the rear of the car stepped out slightly almost in an instant just as I was cresting... I was certain I was going to spin out, but to my surprised, the car literally floated around the corner with the rear slightly hanging out and it is impossible to describe, but it felt so solid, locked in and stable it was unreal... the car never altered its lean angle on the suspension or the longitudinal angle relative to the road... It was drifting, before drifting was popular... and it the fastest I had ever taken that corner.
Later, I was talking to my brother in laws brother who raced Datsun 510s in SCCA and he said I experience the second way to corner a car, not to ease slowly into the steady state, fighting the ragged edge of traction, but to "set the car up" angle and suspension loading before the car even got to the corner and ride that setting all the way thru.
It sounds almost like initiating the lean on the bike with the coutersteer is kind of like "setting the car up" before the corner, technique... and once in the corner, either on the bike or in the car, you used other means of control (feathering throttle, body english etc for bikes, and easing off the steering and throttle for a car) to make small midcorner adjustments...
THe funny thing is that I was never able to recreate that corner that way ever again, because it required a sharp jerk of the wheel that felt like momentarily upsetting the suspension in order to get it quickly settled into its groove... probably what people who are nervous about countersteering feel on the bike...
Damn rabbits...
and, "Doing fast laps is a very violent affair, it just doesn't look violent" and my personal favorite... "To be fast on the track, you must be slow in the cockpit" 
