I had read the reviews of the Apple case before I purchased it. I knew about the problem with the dock, and went ahead and purchased the case and dock anyway.
This problem is caused by about an inch of the casing's protruding rubber edge on each side of the docking point, which prevents the socket of the dock from properly mating with the port of the iPad. I used an Exacto knife to simply slice off an inch of the protruding rubber edging on each side of the iPad's port, and the cased iPad now fits into my dock and makes a connection. I have been testing the connection, and it seems, so far at least, to be constant.
There is, however, a downside. The cutting away of those two inches of rubber makes my case no longer fit the bottom of the iPad as snugly as it once did. That could be the reason why Apple's designers preferred not to leave a three inch wide slot open for the dock. For me, it was a tradeoff -- a less snug fit in exchange for use with the doc.