Hi, I had this type of problem, only it was intermittent. The LOGIN icon appeared if I logged out of FB and my site, then refreshed my webpage. If my session timed out, or I just logged out of my webpage and NOT FB, the text "Login With Facebook" appeared in place of the icon. Regular logins (Username & Passwd) still worked, but I could not use the JFBCLogin when this happened. Unless I logged out of FB completely, this problem occurred 100% of the time.
When I upgraded to 3.0.2, I used the new Upgrade Method -- i.e. I did not uninstall the JFBConnect component, modules, and plugins. After playing around with the problem trying to determine a cause, I finally uninstalled all parts of the component then reinstalled JFBConnect, including JFBCInvite. Since then, the icon has worked as expected.
Hope that might help someone else.
Doug