Jack-
Yeah, I think this is pretty much one of those "to each his own" and "do what works for you" deals (as mentioned earlier).
Two other significant factors for me are a smaller diameter wheel, and no power steering. On smaller diameter wheels, using my thumbs gives me a bit more leverage, more range of motion, and aids in grip. To me, it seams that resting your thumbs on the facing surface reduces sensitivity and leverage (grip), and, is less natural/comfortable.
You are right about the pads of the thumbs, it is just that if you rest your thumbs on the wheel, they are getting input on the vertical plane. If you lock your thumbs (on a wheel with a meaty rim & spokes), they are getting input from the horizontal plane. Also I don't really "lock" my thumbs down into place either. I simply make use of the spoke-to-rim joint.
Try this: raise your hands out in front of you, elbows bent, chest level, as if you are "air driving". Don't just ball your hands up either, pretend you are actually gripping a steering wheel. If you let your hands become totally relaxed, they will naturally fall into that "kung-fu" grip position, which lends itself to driving with your thumbs resting on the spokes.
Here's another one: While "air driving", turn the "wheel" as far as you can in either direction using the thumb-lock method. Now do the same with your thumbs resting on the imaginary facing surface. It should be pretty apparent that you can achieve more steering input (lock) with the thumb-lock method.
For even better results, do this the next time you have the front end of your car up on jack stands, or use the wheel on a driving arcade game.
On the other hand, if you prefer shuffle steering primarily, then resting your thumbs on the facing surface is probably the only way to go.
P.S. -
The only vehicle that self-corrects for skids/slides is a motorcycle. Most cars will have a tendency to return the wheels back to center, due to wheel castor. So, letting go of the wheel in a slide would not be a good thing!