Dave - I'm wondering if you are looking at the page in a logged in state? As given, the example would only show the user profile edit part if the user is logged in (because if they are not, how would we be able to allow them to edit their profile?). So it is wrapped in the status shortcode. The password shortcode does not need this because it has a logged in and logged out state.
Robin - There aren't many reasons why that wouldn't show. First, I would double check to make sure you have the most recent version of the plugin (2.8.2). Of the top of my head, I'm not sure when the password shortcode was added, but it was in one of the more recent versions. So if you have an older version, it may not be there.
Second, WP runs the shortcode parser only once. So any shortcodes used in your setup must also run the parser to make sure that all shortcodes get parsed. Some developers are unaware of this and return $content rather than do_shortcode($content). I don't think that's the case here as I would expect then that you would see an unparsed shortcode. But just to double check, I would test this out with all other plugins deactivated, just so we can eliminate the possibility of a conflict.