If it is set to Gmail there is absolutely going to be authentication unless they are using aspmx.l.google.com, and if they are using that Server they can only send inside of the Gmail, or the internal domain.
They also have smtp-relay.gmail.com but that requires you to register the printer by specific IP address for authentication, and this is a paid server, so you can't just type it in and make it work. (Could be why the message gets displayed in this case)
Lastly there is smtp.gmail.com and that requires login per send.
GMAIL SMTP settings and limits per server
You might need to look into message body and subject lines for email as they would be different for Alerts, Fax Forward and email. 2 could be filtered or listed as spam.