Wrong. Imagine, if you will, that there are portions of the brain dedicated to marshalling the other portions of the network around- sys-admins. These sys-admins spend the entire day making sure the neural network in your skull runs smoothly. Now, it's getting late. They encourage the boss (consiousness) to leave, go home, see his wife, they can close up shop just fine thank you very much. Your consiousness steps out, and then what happens?
What do sys-admins do when the boss goes home? The lan game, duh! They boot up a game and give it a run, messing with your head. REM sleep is when they're playing something that uses alot of bandwith. At that point, the logfiles start noting some of the packets, and that's where dreams come from.