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All that option does is create a .htaccess file which asks your web server (Apache) to ask browsers for authentication (a username and password) before accessing any file in the administrator folder. If you sometimes get unstyled pages it means that your browser doesn't communicate properly with your server. As a result the authentication is not sent which, in turn, results in the files not being loaded.

The most likely culprit for this -which I can't test with your images- is that you have filled in the $live_site in your configuration.php. If $live_site does not include the www part but you access your site with www you will get broken images since your browser sees two different domains. Also applies vice versa. The correct way to do it is to leave $live_site empty and stick with one URL (either with or without www) to access your site's administrator.