I've run into this before, where they didn't want to use a secure password &/or lock down their computers.
Then it happened our website had been hacked into (not b/c of a password breach, but b/c of flawed component/module for the CMS that we used - but that's a different story) and in a few different occasions, people have logged into the exec's computer to view a few inappropriate things.
The reason for this explanation is to say that it wasn't until this and a few other case studies that I brought to their attention that they understood just how important it is for secure passwords.
As a solution, you may try to do some research on case studies where a breach has occurred on systems or sites where the information stored or protected wasn't terribly important, but the damaged cause and money it took to recover was substantial - such as someone setting up a phishing scam on your site, the holding hostage a server or site & having to wipe clean the whole box to start over, or some other type of breach.
Anyways, take it for what it's worth.