Users can use another user's e-mail account to open Tickets without a identity confirmation

This should be addressed.

Hello,

It is possible to disable the email field for the user on the new ticket form using portal customisation option available on the Estate plan. 

You can include this code snippet in the new ticket page under Portal pages option.

<script>
jQuery(document).ready(function(){
jQuery('#helpdesk_ticket_email').attr("disabled",true);
});
</script>

Cheers!