When I send an email with the PHP Swift mailer to this server: smtp.exchange.example.com like this:
// Load transport $this->transport = Swift_SmtpTra
You perhaps use the wrong username.
I had a similar error. Ensure you're not using uppercase while logging into server.
Example: JacekPL@lala.pl
If you use ->setUsername('JacekPL'), this can cause an error. Use ->setUsername('jacekpl') instead. This solved my problem.
->setUsername('JacekPL')
->setUsername('jacekpl')