I don't know if people are still interested in this. I have just run into the same problem while migrating to a new server (and new configuration, for example with backups).
I have disabled exim4 by doing
Code:
update-rc.d -f exim4 remove
I have just finished installing, then will be running my first backup. I am also going to change the /etc/backupninja.conf reportemail setting to a full email address on my zimbra server.