I think you got it wrong. Baron gave transaction details of 3 transactions that sent money from LR account U1172929 to LR account U8227430, which I can verify that it belongs to MtGox (it's what the page for depositing funds on MtGox links to). Baron can probably show that LR account U1172929 belongs to him by offering to send a few cents to anyone who asks. The sum of the money sent to MtGox from U1172929 is 74616 USD.

According to what I read on this thread, what Baron is accused of is the stealing of 9000BTC by guessing a MtGox user's password. The evidence is in the Bitcoin block chain because the money was sent directly from MtGox to Baron's Bitcoin addresses (19n8ogD8imviHn9iZSpmUgdZqjTuDxzDwv and 1DVQEpTFjxYpZMVy4Bam9MCxeGEtmMmQCh). This is why Baron is believed to be the thief.

MtGox also accuses Baron of other things, but the evidence for those things is only in MtGox's server logs.

Now, Baron, in his defense, says that the money was offered to him by someone on IRC, in exchange for USD from his LR account. Obviously, the only way to prove this is to see evidence of Baron's LR transaction with the real thief and then to follow the money.

There is still the scenario that MtGox is the scammer in this case, who may be trying to gain a large sum of money, by sacrificing a smaller sum of money.

Also, another way to see if the person on IRC exists is to start asking people on IRC whether or not they have kept logs of their PM conversations at around the days when the 3x3000BTC transactions took place (the thief may have been PMing people, making his offer). A person who has "hacked" into a MtGox account and wants to sell the money may have been careful to make his offer only in private (as this is IRC, as I understand), so nobody can "see" him. Did Baron go to #bitcoin-otc? If so, he must have not followed any #bitcoin-otc "rating systems". Possibly, the thief sent the money first (not his money, anyway) and Baron just felt "obliged" to give something in return.

A protocol analysis of the SSL communications between Baron and MtGox probably won't be any good, because of the "Diffie-Hellman key exchange". A digitally signed such log would prove what Baron did with his money on MtGox, and how much is his. This is analogous to receipts.

Another way to go about this is to search for everyone with whom Baron has traded on MtGox and try to get statements from them. But only MtGox has that information now, in his own files, as Baron is locked out. It may be gone already, if MtGox is the scammer. This is probably the reason Baron wanted to take screen-shots.

I think the main reason that the dispute can't be resolved right here is that there is difficulty in proving that the people who speak are separate people. But then, in RL courts, there is always the problem of false witnesses.