Jenni,
The Facebook comment box is only available to make a post if you are logged into Facebook. If you aren't logged into Facebook, the user can see any comments that have been made, but won't be able to post a new one.. until they log in to Facebook.
Please note that the comment box does not change whether the user is logged into your site at all. All that matters is that the user is logged into Facebook.com, regardless of whether they've used their FB credentials to login to your site.
Once logged into Facebook.com, there should be an option to Post to Facebook. The user has the option to use that checkbox if they want the comment to show on their own Timeline.
I hope that helps,
Alex