Wallet software changed over time. Wallets used to not be deterministic in the 2010 versions, so if you took the same wallet to different computers, it would generate a different set of keys after the first 200 were used, even with the same initial wallet. This wouldn't explain Stoneman unless he had over 200 transactions with the same wallet, which is pretty unlikely since nothing like that has been tracked and it would leave evidence. The software has since been changed since so this issue does not exist -- wallets since then generate deterministic keys on different computers to avoid this issue.
The very honest answer is that Stoneman was a bloody liar. All transactions are visible to everyone, and Stoneman used that ability to claim bitcoin that were not his after that transaction. He gave the wrong details, being very slightly off, and only one person back then called him out on it. If you look it up, the transaction was for 8,999 and not 8900 like Stoneman said. This is a common scam tactic - giving the wrong value, but just wrong enough - it gives plausible deniability if someone can prove him wrong without a doubt and he can say that his was a slightly different thing, but also gives him the ability to be super disruptive if no one has sufficient proof.
He argues that it was a double spend, which he would have evidence / know if it were -- but then changes his argument to the explanation above. He offered no proof that he that owned the original nor final wallet. I wouldn't be surprised if one of the first exchanges shut down from later actions by Stoneman by reversing paypal payments, which favored the buyer claiming fraud - but in itself enabled the possibility of fraud.
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