Postfix: how to force MX lookup for 'local' domain?

[random.guy]

Let's say my server's hostname is site.com. I also run various web based software packages, which send out e-mail to customers. This works great. The problem is that my server also sends out e-mail to user@site.com.

The problem is that the site.com e-mail is not hosted on this server, it's actually hosted on a 3rd party e-mail server, so I am not getting these e-mails. Is there a way of forcing Postfix to use the MX records for site.com, even if this is the local name of the server? The server will not be receiving ANY e-mail, just send out.

Thanks!