Just wanted to get back in touch with you. We've been testing every way we can, and we can't recreate some of the things you mention above. From here, we'd ask if you could at least send us a link to your site, and if you're ok with it, a super admin account so we can look at and recreate all of your settings on a development machine.
We've configured our JFBConnect similar to how you mention above, and think CB is the same. When we try to log into our development site, we get 2 popups (as expected). The first is for permission for name, email and 'basic' information. The second is for extended profile information- to import into CB. If we deny the first permission box, we're simply returned to the page we tried to login from. If we deny the 2nd box, we are allowed to proceed to registration. This is normal because the "Require Profile Data Permissions:" is set to No. If that was Yes, then there would only be one permission popup with all permissions in it.
After we register, even though we denied the 2nd pop up, the Joomla user has it's Full Name correctly filled out from the FB information. CB also has the Name, username, and email fields correctly filled out. We're able to 'save' this user without making any alterations.
With our situation noted, this is where it becomes important to see your configuration because either something isn't working properly with JFBConnect, or there's some settings in JFBConnect and CB that we haven't tested yet.
Finally, I looked back through the other thread you've posted in, and noticed this was a problem back in August as well. Was this ever cleared up over this time, or has this been a constant issue? Know that answer may help us determine a cause and solution:
www.sourcecoast.com/forums/topic?id=1200
Thanks!