Could you try to deactivate any other plugins that may affect your site’s commenting and log in system? By default, Twenty Twelve displays a link to allow you to log in to comment, as you can see on this screenshot: http://i.wpne.ws/MGU3
Jeremy, I’ve got a development site at http://drfragen.info. The only plugin active is Jetpack theme is TwentEleven. Still, with only registered user allowed to comment checked, Jetpack comment not working.
If you want an admin login to this site let me know where to send it. Thanks for looking into this.