Earlier quoted context omitted.
What do you expect? Uber has no way to authenticate you if email doesn't work. Technically they do - they could send an SMS to the registered number, which as OP points out, is unique.
There's also more than just phone. Could use the full credit card #. They can also send the device a push notification with a security token and have the user reset password with it in lieu of an email based token.
I doubt they're storing that.