What Paypal cares about is whether the owner of the account was in control of the account during the time the transaction was made, and you need to prove that beyond reasonable doubt. Notes/ToS don't do anything, contrary to popular belief.
@OblivionRage also told me that he's lost chargebacks even when he's supplied ID proof, and I've lost chargebacks even with the IP address/location of the scammer. What I've been doing to fight chargebacks is sending an email to the address associated with the Paypal account asking them to confirm their identity and that they've authorized the transaction and sent the correct amount of money. If possible, waiting a day before delivering the goods might also help, because a high value transaction will normally trigger alerts if someone's account was actually hacked.
So far, this strategy appears to work.
This was a credit card/bank chargeback, which are notoriously difficult to win (compared to "unauthorized claims" which are already quite difficult to win in the first place)