I tried sending an email like user@ [123.34.123.123] as it states in the postfix tutorial, if I am not using a DNS and therefore am not using MX records to relay the mail, and it does not work.

So I've had Postfix set up for a while on all my hosts to forward root email, notifications, that kind of thing. I've had it relaying email directly and via SES at different times. But the ...