"Return to sender, address unknown....-- "Return to Sender", written by Winfield Scott and Otis Blackwell, recorded and published by Elvis Presley
No such number, no such zone."
A Rackspace rep was saying that the reason why I was having difficulties in sending email out from the website was because outbound email has to go through the same server as what one uses for inbound email. That's typical but not required.
Even though I'm using Google Apps, not Rackspace, for my inbound email, I tried using the Rackspace control panel to create an email user who will never receive mail, (because my mail doesn't go to Rackspace). I configured the username "sender" (at aboutth.is) with the full name "Elvis Presley", and that worked; I'm now able to send mail out (from the unmonitored From: address of noreply at aboutth.is) through the AboutTh.is website! :-)
I also added an SPF record to announce that Rackspace is permitted to send mail out on my behalf.