There is no outbound mail sent throught he server from the domains that have external mail servers, but I wonder if there is something odd that explains what is happening.
Here's a sample from the mail.log - I've replaced the client's details with clientname - the main account that is clocking all the mail (but not sending or receiving any) is hairydog.co.uk. The server was set up as hosting.hairydog.co.uk. Is this being counted as hairydog.co.uk mail in the stats?
Jan 18 01:39:52 hosting postfix/local: B10D33C04F: to=<email@example.com>, orig_to=<firstname.lastname@example.org>, relay=local, delay=69, status=sent (forwarded as 96A903C138)