The API method I gave you is for automatically posting on the user's behalf to their wall. That's not something that can be done without the user having granted the publish_actions permission for your app, and that's only done after they've logged into your app/website. If you could post to anyone's wall that was merely logged into Facebook when they visited your site.. well, you can imagine the abuse that would happen.
For users that aren't logged in, you could show a "Post to Wall" option where the user can choose to post the message to their wall. This can't be done through the API though as you wouldn't have the authentication token required to do it that way. For showing a feed post popup, you can use the following link:
<a href="javascript:void(0)" onclick="jfbc.social.feedPost('I took a quiz', 'caption for quiz', 'description of quiz', 'http://site.com/link-to-quiz', 'http://site.com/link-to-image-for-quiz.jpg')">I took this quiz</a>
That will bring up a popup with the parameters set above (title, caption, description, url, image) that the user can choose to take to post to their wall.
With that code, you could have 2 options in your code: a) auto-post if the user is logged into your site using Facebook or b) show the link to let any other type of user (guest or joomla-only user) make a post.
I hope that helps give you an idea, but let me know if you have any questions!
Alex