The issue is, from what I see, that AMEX has accepted the hotel's submission of evidence as enough to support that the claim was charged validly. That is the same in Australia as anywhere else.

The process once the evidence is provided ( same with AMEX as Visa I believe ) is to write back to the card company detailing how the evidence provided by the retailer is deficient/invalid. The card company will then take this and re-investigate further

Just claiming "It is not mine" is not sufficient even in Australia. There is a process to follow if the retailer does substantiate on the initial chargeback request.