With MySQL 5.6 every run of automysqlbackup will generate the following warning (and potentially an error email):
Warning: Using a password on the command line interface can be insecure.
This is because automysqlbackup uses username and password directly on the mysql command for the connection.
Here the problem has been solved:
http://www.redeo.nl/2013/11/automysqlbackup-warning-using-password-command-line-interface-can-insecure/
But I don't know if this is the cleanest solution.