If that message is being displayed by the backup_mysql, note that sometimes it's a misnomer ... there's a tiny error in the logic that displays the message, in that it doesn't always detect only what it's supposed to.

You're only concerned if "exec" is disabled. "shell_exec" is not used by this script, so is not a problem. Thus, if "exec" itself is not listed, you should be able to run it (assuming the host has fixed everything else properly too)