The problem was that once I had entered a user name and a password for the SMTP connection, the password never was removed from the underlying storage - the bamboo-mail.cfg.xml in BAMBOO_HOME. In the UI, it looked like there was no password set (the text field is empty), but when I push the Test button, it uses the password saved in said file.

Now, since the SMTP server I tested with was "no authentication", it failed because the password was sent.

affects 4.4.something