Surely Amazon have pretty clear evidence in front of them. Someone's reported their kindle stolen, they see the kindle registered in someone else's name shortly after that report, the police have contacted them. Amazon can surely create their own paper trail - verifying the identity of the police first.
Besides, the other post implies that they're saying there's no hard link between the kindle and the account. That's probably front-line support failing to get a message higher than their lazy supervisor.
Anyway, I disagree with the sentiments here and in other replies. There are privacy warriors - quite rightly so - but there's also blatant common sense. Amazon should be applying that here. Putting on a tin-foil hat and saying "but what if..." isn't always a sensible thing to do.
If you commit a crime and submit evidence of it to my web service, you can be damn sure I'm passing your details to the police, so long as it's legal for me to do so.