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.
Right, but the problem is that it traces to a MtGox account
that is not yours. MtGox uses Bitcoin accounts to receive money. When they spend that money, it comes from their receiving addresses. So your payment went to someone else's receiving address.
I have a deposit address at Mt. Gox. Say I send 10 BTC to that account. The 10 BTC will be sent to *my* Mt. Gox receiving address. Now, say you send 1 BTC to SD. If it uses some of my 10 BTC, which it might, then your transaction's sending address will be my transaction's receiving address. To Mt. Gox, it will look like I am depositing more Bitcoins.
IMO, it is SD that is broken. It does not make sense to automatically send Bitcoins to an address just because it sent Bitcoins to you. There is no way to know that the recipient will bear any logical relationship to the actual sender.