Drupal 7: Menu item being accessed even with false access callback?
user_is_anonymous() returns TRUE if the user is a menu administrator: see function user_is_anonymous

Try user_is_logged_in() instead, e.g.:

function the_permissions_function { 
    $isLoggedIn = user_is_logged_in();
    if ($isLoggedIn) {
        return FALSE;
    } 
    return TRUE;
}