Makes sense. If the NETWORK is down, meaning the LAN, you will not be able to E-mail no matter what. I haev actually had something like this happen. A user claimed they could not SEND/RECEIVE mail, and they told the Helpdesk by sending an E-mail. We weren't sure how to respond without insulting the requester.
If the email system is on the LAN and the internet connection goes out, you can still email the IT/IS department for assistance. If the problem is not with your terminal, they probably already know about the issue. If the problem is with your terminal it is probably a bad NIC, switch, or an ID10T error.