From everything that I've read while investigating this issue, the ability to be able to post comments anonymously was a Facebook Application setting. I say 'was' because the option is no longer available in the Facebook settings. It used to reside under the Settings > Widget tab. We don't see a difference between their code and ours for the comment module, so maybe it's possible that the demo page you mentioned above had the comments set up for anonymous comments when the option was available. Here's a long thread on the facebook developers forum regarding the comment boxes and it seems that a lot of people have the same issue -
forum.developers.facebook.net/vi … 9&p=1. We'll keep investigating, but don't have a solution yet.