Good thread.
I look at this from purely a technical Newtonian viewpoint and here is my shortest explanation of how I understand it.
With a car we have 4 wheels, so to corner we turn the front wheels, and the rear wheels follow. More mass gets distributed on the wheels outer side of corner and less inner side, due to the centripetal force of the velocity in the curve.
With a bike, two wheels are missing, so if we turn the steering left, the centripetal force will make the bike lean right. Now we have to turn the steering slightly right to correct and the bike will turn right. The bike has to lean to the right to counteract the centripetal force of the curved path. In fact, you may not realize it, but while leaning over you are actually turning the steering to the right, balancing the centrapetal force with the amount you are leaning and turning in. We learn how to do this as kids riding bicycles, but we never think about how it actually works. It just becomes natural. Don't believe me, do a sharp corner at 10 mph and concentrate on what is actually going on.
To drag a knee and an elbow for Mr. Spies, you are displacing the center of gravity of the bike as much as you possibly can towards the inside of the curve, this helps counter acting the centripetal force, reduces your lean angle, makes the turn safer and faster.
If you move the center of gravity to the inside of the curve as much as you can by displacing your body and the bike leans as much as it can, some body part will touch the pavement, better your knee than something else.
That's my story and I'm sticking to it.
By the way, it took Orville and Wilber Wright (fist flight North Carolina) some time to figure this out in the early 1900's.