Outgoing Email Settings for SharePoint Services

The SharePoint server I inherited would not send outgoing emails. The SMTP service was installed on the same server and all the settings looked correct. Well, that is what I thought until I ran through the instructions found in the TechNet site here:
http://technet.microsoft.com/en-us/library/cc287879.aspx

In the section for configuring the SMTP service, steps 8 and 9 talk about setting up the relay permissions. Make sure you either include the server name of the localhost or select the All excepts the list below option. You would think that localhost would be able relay through its own server without any changes to the settings, but that is not the case.