Tim Cook Says Apple Can't Read Users' Emails,
No he didn't.
Apple previously said that even it can't access iMessage and FaceTime communications, stating that such messages and calls are not held in an "identifiable form." [Cook] claimed if the government "laid a subpoena," then Apple "can't provide it." He said, bluntly: "We don't have a key... the door is closed." He reiterated previous comments, whereby Apple has said it is not in the business of collecting people's data. He said: "When we design a new service, we try not to collect data. We're not reading your email."
He said they cannot read iMessage and FaceTime, and they are not reading your email. That is a very important distinction. It might be one he was hoping you would miss, and you did miss it, but he did not say they can't access your email.
And I'm not blowing sunshine up his skirt. I came here intending to kick him in the balls (metaphorically, of course) for lying, but he didn't.
Pro-tip: If any system includes a password recovery mechanism that allows you to get back messages, then the administrator of the password recovery system can read your back messages.