So, for the sake of argument, let's say Kirkham (asphalt) has a ct/km of 11000.78 (average of pre-and post runs) and Cleveland (concrete) has an ct/km of 10995.915.
The difference is 4.865/km or 1.6 counts over the length of the course. That's about 30 degrees of wheel movement, or 8 inches on the ground if I'm figuring it correctly.
Not having read the measurement procedures manual lately, I can't remember the proper braking procedure, or if it's mentioned at all. Is the front brake used while measuring? I can see where braking would induce some wheel slippage, but 8 inches of it on a cal course? Doubtful that braking alone is the cause of the discrepancy.
Interesting stuff. Might be worth fitting a counter to the rear wheel to see what effect propulsion has on the count, and how this varies on different surfaces.
In reference to automobile (or any pneumatic) tires, the carcass is only thicker because of the larger amount of fabric required to support the load. Like a bicycle tire, the load is not borne by the bottom part of the sidewall (except in the case of modern run-flat tires, and there only for short distances at reduced speeds) but rather by the top portion. The air pressure allows the tire to maintain a round shape, and the weight hangs from the top portion. Think of it like a bicycle wheel. The spokes aren't strong enough to support the load in compression, but in tension they hold it easily. The "spokes" in this case is the fabric inside the tire, and the "rim" is the air pressure supporting it.
As to contact patch slipping, it's a larger patch and tends to move around a bit, especially on the steering axle. Higher speeds and greater loads also induce more slipping than you'll find in a bicycle tire. However, it does seem that the Cf plays a significant role, as Pete's data shows.