From the article:
'The only solution to Facebook not knowing who you are is to delete all Facebook cookies.'
I think that if you set the cookie permissions correctly, you should be able to use fb, and not have the cookies track you after you log out (In Firefox)
From the facebook home page, right-click on an empty part of the page, and select 'View Page info. The select the Permissions tab.
there is an option for 'Set Cookies'
Set it to 'Allow for session', and the cookies should be deleted when you logout.