Actually there is an option to select whether the ´mysql´ database should be included in the backup or not. To put it another way: you can backup 'all data' or 'all user data' depending on what is most appropriate for you. If you are not the server administrator you should be careful about backing up and restoring the ´mysql´database (if you have the privileges required for this).

Also note that the ´Information_Schema´ database will not be backed up using neither 'all data' nor 'all user data' options. This database is a read-only database created automatically by the server. It only contains temporary tables of server 'metadata' only (= 'data about the data'), no real data. However you may specify the ´Information_Schema´ database individually for backup if you should want for some special purpose.