First off, I'm still quite new at all of the Facebook APIs and I even tried making a site using this method, but I gave up on it because I had more important things to do. Also, I understand the origanal Facebook documentation sucks and can even be contradictory.
I think it might be (1) missing the Facebook Javascript SDK or (2) your site might not be logging them out as well (depending on how you coded it). More in depth...
On that one specific page, I did not see the Javascript SDK:
http://github.com/facebook/connect-js/
Code:
<div id="fb-root"></div>
<script src="http://connect.facebook.net/sr/all.js"></script>
<script>
FB.init({
appId : 'YOUR APP ID',
status : true, // check login status
cookie : true, // enable cookies to allow the server to access the session
xfbml : true // parse XFBML
});
</script>
Try using the Firebug plugin in Firefox, this should show any errors in the Javascript. (Sorry the Mozilla site is in Serbian from this url because my computer is too. Try changing the "sr" to "en" in the url)
It could also be that your site requests them to login via Facebook, then Facebook sends you perameters that get turned into a Sesson. When they click the logout button, the Facebook session might be destroyed but not the one for only your site.
Also check out this file:
Code:
http://www.megaupload.com/?d=UVH7M25X
---------- Post added at 05:50 AM ---------- Previous post was at 05:44 AM ----------
Also, sometimes random things don't work in diffrent browsers (or at least on my computer). An example is when I go to a 3rd party "Like" site and I click the "Like" button, it doesn't do anything (when logged in) or I get a login window from Facebook that turns blank after logging in. This only happens in IE for me but not Firefox. This probably is not a factor but is still good to know.