Apple is partly to blame here. One big problem is that there are so many false positives for the "A new iPhone/iPad has access to Facetime/iMessage on your account" warning -- a message that can easily be triggered on all your devices by an automatic upgrade on one of them. If you have an iDevice that is online but not used often, you'll be surprised by this message every few months.

This problem either causes undue concern on behalf of the account holder, or trains them to dismiss these messages without verifying the potential intrusion. Neither are good outcomes for security of the Apple account.