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You couldn't do that, because only one of the transactions would actually be in the block chain.
That would mean that valid transactions do not appear on blockchain - I consider this rubbish.
Both transactions would be in the blockchain - the initial withdrawal and then the re-withdrawl request several weeks later which mtgox would have allowed.
I agree with this.
One needs to pair those two transactions (find them in the blockchain). ...
and
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This means that it's not possible for both transactions to be in the blockchain, so people/organizations affected by this won't have to go through the blockchain to find people who double-withdrew, right?
Yes. Only one can ultimately exist in the blockchain.
My understanding is that indeed only one transaction gets registered in the blockchain, but there seem to be different takes on this issue.