Two queries – one with checkbox ticked, one without – comparing meta_query

If you only have two types (directors and none directors and you allready get all of the directors you can simply use the post__not_in parameter, ex:

// Get your directors just like you do now
// $directors = get_posts(array( ...
// Then create a simple array with only the post id's of the directors.
$directors_ids = array();
foreach($directors as $d)
    $directors_ids[] = $d->ID;

//then you can get all of the people who are not directors using:
$people = get_posts(array(
    'post_type'      => 'people',
    'orderby'        => 'meta_value',
    'meta_key'       => 'last_name',
    'order'          => 'ASC',
    'posts_per_page' => -1,
    'post__not_in'   => $directors_ids
    )
);