I just ran into this same problem.
My zimbra server is on the Internet, separate from my LAN. I set the trusted networks on the server so that clients on the LAN could use the Zimbra server as a SMTP server without authenticating. However when this value is set, you have to include the Zimbra server's IP address as a trusted network. If you don't set the server's IP as trusted it will reject any email sent outside of the server.