Spence,
I don't know how much better I can say what you've pointed out about the one-hand cut. You are 100% correct.
Let me explain it like this. We will assume the dealer is right handed. After a brief scramble the cards will be gathered together using both hands, (cards will be facing away from the dealer), that's right...away from the dealer. The solid deck will be face down to be followed by: riffle, riffle, 2 or 3 strips (or box) the final riffle, and a right-hand cut onto the cut card that is placed into position beyond the deck by the left hand. Whew...Using the right hand again, place the remaining portion of the deck on top of the first half, lifting the complete deck (still using the right hand only) and place the deck into your left hand while securing the deck with the dealers grip! You are now ready to begin pitching the cards. When done properly, the whole process is completed in under 12 seconds! It takes longer to explain it, than it does to execute.