BR,
I'm not sure. I can't recreate the issue. I'm always seeing the Activity Feed and Recommendations Bar whether I am logged into Facebook.com or not. Just to be clear, I'm *not* logged into your site, just Facebook. Those modules shouldn't care whether you are logged into your site though.
Is it possible to test on another computer? There's nothing I can see wrong with the HTML/widgets on that page that would cause the issue you're mentioning.
Thanks,
Alex