You need to include comments functionality via
comments_template(), because this function doesn't merely include the
comments.php, file, but also handles all of the querying and functions required for displaying comments.
While the Codex doesn't really get into details, you can see, by looking at source, what's going on:
* Loads the comment template specified in $file.
* Will not display the comments template if not on single post or page, or if
* the post does not have comments.
* Uses the WordPress database object to query for the comments. The comments
* are passed through the 'comments_array' filter hook with the list of comments
* and the post ID respectively.
* The $file path is passed through a filter hook called, 'comments_template'
* which includes the TEMPLATEPATH and $file combined. Tries the $filtered path
* first and if it fails it will require the default comment template from the
* default theme. If either does not exist, then the WordPress process will be
* halted. It is advised for that reason, that the default theme is not deleted.
* @since 1.5.0
* @global array $comment List of comment objects for the current post
* @uses $wpdb
* @uses $post
* @uses $withcomments Will not try to get the comments if the post has none.
* @param string $file Optional, default '/comments.php'. The file to load
* @param bool $separate_comments Optional, whether to separate the comments by comment type. Default is false.
* @return null Returns null if no comments appear