A Bitcoin exchange can't work any other way. Otherwise, every single trade would have to be accompanied by a blockchain transaction to move the funds to "your" address.
Yes, but MtGox does log my send transaction, and does know about the received transaction from SatoshiDice. For each transaction they know about the exit point, the following entry point, and they can trace the final point at an MtGox address tied to an MtGox account.