At a minimum Amazon should have to help clearing up the issue. I guess some entities are above the rules most of us have to live by. Same with hospitals that can repeatedly charge bogus items without any consequences.
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.