If you don't want to lull your users into a false sense of security, then why doesn't the "save password?" dialog have a disclaimer reading, "All saved passwords can be viewed at chrome://settings/passwords". This simple notification would go a long way towards raising the level of awareness you seem to assume the average person already has.
Then they might chose to use IE instead, which doesn't show that disclaimer yet is no different. The teaching that needs to be done is that letting a bad guy access your computer unlocked is game over.
Are you on XP with IE6 or something? IE uses the Windows credential store nowadays, which requires you to reenter your logon password before it will expose your password....
