The best thing to do is exactly what they said, file a chargeback and eventually Amazon can take action.
You'll notice the person running the website never cooperated with answering Amazon's questions, it's no wonder they didn't work with her. If you don't want to work with the merchant, then contact the credit card company. Not hard to figure out.
I think the real solution would be for them to just provide an auth mechanism for people to prove they are the CC owner so they can remove the payment method from any accounts and not give out any info on the name or email on the account. I've seen a few things that use a small charge that gets refunded and you enter it back in the app as a 2FA.
Where do you see that? The only question asked was the phone number the scammer used for the scam account.