OK, I did one more test:
I also use the plugin of "post notification", so I used its test send feature and it failed, using the following (edited) data:
"
The mail has not been sent!
PHP-Mailer - Dump:
object(PHPMailer)#<number> (<number>) {
["Priority"]=>
int(<number>)
["CharSet"]=>
string(5) "UTF-8"
["ContentType"]=>
string(9) "text/html"
["Encoding"]=>
string(4) "8bit"
["ErrorInfo"]=>
string(35) "SMTP Error: Could not authenticate."
"