One Users Email not working for 'test'
I think that message is telling you that the email that your smtp server is trying to send to is "EMAIL ADDRESS HERE", which is clearly a placeholder that needs to be filled in. I'd check the record of the contact who is unable to send themselves a test email for fishy bits (e.g. the primary email address, which perhaps got set via an import). If that record looks good, then I'd guess that the email address it's sending to is something unusual for the mail host machine and has a badly configured forward or something like that.

But no, you don't need to do anything special to enable test emails.