A suggested improved customer interaction with the Apple Store

Apple's email was straight forward and to the point (high signal to noise). The "solution" needlessly tacks on boilerplate, and divulges additional information about the user in the email. If someone's iTunes account has been compromised, it is possible that their email account may have been as well. Best not to show too much.

The actionable item in Apple's email is very clear: change my password, and then learn how to be more secure. In the "solution," it is not. You need to "associate [my] new device with [my] Apple ID"? Huh? Do I need to re-register my current device, or what?

I'm all for using Bayesian inference behind the scenes, but don't needlessly flood the user with excess information. Tell them what's up, and what they need to do.

Withholding information could be helpful later, should the user need to verify their identity over the phone (for example).

Sending an email when an account is used for the first time on a new device is not a bad idea, but it could become another hoop for the user to jump through, and again, their email may also be compromised.

Apple obviously knew there was something off. Their systems detected an issue. Detecting an intrusion is obviously not a problem, though I do think your suggestions for detection would be nice.

The way it reacted to an intrusion, however is absolutely unacceptable. Simply informing you that you got hacked after it's already happened is not the way it should have dealt with this. Ideally, it would block the purchase, blacklist the IP, then force you to confirm through an email.

Sure, if your email got compromised too, that won't do any good, but at least it would have tried to stop the unauthorized access.

Another nice thing I'd like to see would be something like Google's two-step authentication, where you would have to authorize the new registration via a previously registered device.