Both display of comments and comment form should be handled in comments.php (or other template designated for that by theme).
While comment_form() function does check if registration is required (and doesn’t output form to unregistered users in such case) wp_list_comments() does not perform such check, since it isn’t in line with native logic of this setting.
I had grabbed copy of Elegant News theme you are using on site and I don’t see explicit additional conditions in comments.php. Either your description of issue is missing some details or is cause by a plugin or other additional code.