Kevin,
Unfortunately, that's not possible with JFBConnect. The comments module is from Facebook, and they allow any to write a message if that user is currently logged in / registered with Facebook. They don't make a determination as to whether the user is logged into your specific site or not.
The benefit of that is that your users can engage with your content without having to have an account. That also helps promote your site since there's less 'friction' to post a comment (they don't have to register/log in). Of course, it also means the user has to have a Facebook account to do so.
I hope that helps explain. There's not a fix for that issue that we can provide though.
Thanks,
Alex