Display number of comment replies

I want to show the 3 most recent comments and have a small div underneath that shows how many replies each comment has (count how many comments where comment_parent => comment_ID).

I do this by looping through each parent comment (comment_parent => 0) and then for each parent comment, use get_comments(comment_parent => $comment_ID).

Unfortunately the comment_parent is ignored on the inner-loop of each comment and I get returned an array of comments where comment_parent => 0. Why is comment_parent getting ignored?

<!-- DISPLAY RECENT COMMENTS -->
<?php $args = array(
                    'number' => 3,
                    'status' => 'approve',
                    'comment_parent' => 0
                    );
$recent_comments = get_comments($args);
foreach($recent_comments as $recent_comment){
    echo '<div class="front-page-comments">';
    echo $recent_comment->comment_content;
    echo '</div>';
    $parent_comment_id = $recent_comment->comment_ID;
    $comment_meta_args = array(
                               'status' => 'approve',
                               'comment_parent' => intval($parent_comment_id),
                               'number' => 3
                               );
    $replies = get_comments($comment_meta_args);
    echo '<div class="front-page-comment-meta">';
    echo $parent_comment_id . '<br />';
    echo '<pre>';
    print_r($replies);
    echo '</pre>';

    //echo $replies . 'Replies';
    echo '</div>';
}

?>

In the wordpress codex function reference for comments, it looks like the parameter for the parent is not comment_parent but just parent. Which is weird and inconsistent because the return values are prefixed with comment_.