Empty page does not work when set as 403 or 404 page

I dont believe you can override the default behavior of Acces Denied in this way. Access checks happen long before the empty_page module gets its hands on the request.

I'm 99% sure I'm right about this too...

Please re-open if you have any evidence to contradict my comments in #1

Actually this is a legitimate issue. And the fix is quite simple. For D7, I tracked it down to drupal_deliver_html_page() in common.inc:
(... indicates code removed for readability purposes)

<?php
switch ($page_callback_result) {
      case MENU_NOT_FOUND:
        // Print a 404 page.
        ...
        $path = drupal_get_normal_path(variable_get('site_404', ''));
        if ($path && $path != $_GET['q']) {
          // Custom 404 handler. Set the active item in case there are tabs to
          // display, or other dependencies on the path.
          menu_set_active_item($path);
          $return = menu_execute_active_handler($path, FALSE);
        }

        if (empty($return) || $return == MENU_NOT_FOUND || $return == MENU_ACCESS_DENIED) {
          // Standard 404 handler.
          drupal_set_title(t('Page not found'));
          $return = t('The requested page could not be found.');
        }
?>

The if (empty($return) check always returns TRUE because our menu callback is always empty. :)

<?php
function empty_page_empty() {
  return '';
}
?>

All that needs to be done to fix this is changing the return to ' ' (a space) instead of ''. This should also be the case for D6 version. I don't have time to commit this right now. bleen18 if you feel like making this change for Drupal 6 and 7 dev versions, go ahead.

Nice catch carn1x.

I committed this change to both (7.x) and master (6.x):
http://drupalcode.org/project/empty_page.git/commit/f25e49a
http://drupalcode.org/project/empty_page.git/commit/10ef158