The message log feature lists every SMS and email dispatched by the scheduling system. It doesn't necessarily mean the message arrived to the recipient, only that it was successfully dispatched.
If the information is correct and the message wasn't delivered then something stopped the message after it left the scheduling system. Our ability to help will be extremely limited. Ask the user to check their account spam folder and to check or any blocks for the senders email address. Since we provide your own isolated scheduling system a few email mail providers by default block senders they don't recognize and you may have to ask that email provider for assistance.