Ok, seeing as how I have no clue what is wrong, and after looking into things a little more, I think there is a serious configuration error...
I've got a test account set up and have been trying to mail between that and a test account I use with gmail.
I set up a server with ISPConfig3 on Ubuntu 12.04 for a client using the Perfect Server Tutorial for BIND, Apache, Postfix, and ISPConfig3....
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