You can't because #1 was recorded onchain, not offchain.
They sure were, but now my balance is with MtGox, not the blockchain. Your argument is that MtGox's systems are so inept that I can buy something off them and then send those bitcoins somewhere else (non-cartel). I'm pretty sure those programmers would be fired.I was expecting you to say that
You are confused.
And I know exactly what your confusion is, because I used to do techsupport.
Listen up. When the customer spends on the cartel, the offchain transaction would happen at that point. So the Bitcoin blockchain still shows the customer owning the coins. Whereas for your MtGox example, the Bitcoin blockchain shows MtGox owning the coins. So you are comparing two different things, apples-to-oranges.
It has nothing to do with ineptness once the coins are inside the cartel or MtGox. Both are managed correctly and no double-spends. The double-spend is due to the Bitcoin chain showing the customer still owns the coins in the cartel case, so customer can issue a Bitcoin chain spend again even while spending the coins in the cartel chain simultaneously. Whereas for your MtGox example, the Bitcoin chain shows MtGox owns the coins, so the customer can not issue a Bitcoin chain spend again.
In your 'cartel' situation, who controls the private key for the customer's wallet?
If it is the customer, then the cartel website cannot sign a spending transaction, and so cannot withhold it from the network, it would have to be send by the customer.
If it the cartel, then the customer cannot sign a double-spend transaction.