hook_form_alter problem

Hi,
I'm using a module which uses the form_alter hook to edit a form, and add a custom 'submit' function.
Unfortunately the custom submit function never seems to get fired.
Debugging shows that the alter_hook function is fired OK and updates the $form['#submit'] value successfully. The function is never called though, when the form is submitted. Any idea why that might happen?

The module is user_delete 5.x-1.2, which allows the user to delete their own accounts. The submit function is added like this:
$form['#submit'] = array('user_delete_submit' => array());
The function user_delete_submit() doesn't seem to be called - instead the user.module function user_delete() is called.

Thanks.