Hi John,
I take extra special care when creating ListMail to not provide opportunities for hackers to exploit. Your next line of defense is at the host level, such as with user permissions, system updates, etc. While these things are important your client may be a bit paranoid.
As long as your host stays reasonably up to date on system updates you should be fine. Even in the event of a hack it is unlikely (but possible) that your data will be accessed directly.. It is more likely that your server will become part of a botnet, exploited for it's power as opposed to its contents.
Regards