Why does my script does not run in runlevel 0?

I made a script with following LSB header

#! /bin/sh
### BEGIN INIT INFO
# Provides:          updateservice
# Required-Start:    $local_fs $time $network $named $syslog
# Required-Stop:     $local_fs $time $network $named $syslog
# Default-Start:
# Default-Stop:      0
# Short-Description: Update Service
# Description:       This script is meant to update and upgrade
#                    the system. It uses apt-get.
### END INIT INFO

placed it in /etc/init.d and created the links with update-rc.d and got the one I wanted to have

 lrwxrwxrwx 1 root root 19 Nov 29 13:08 /etc/rc0.d/K01update.sh -> ../init.d/update.sh

.... but: The script ist not executed at shutdown. Why?

Running /etc/init.d/update.sh stop manuallly does exactly what I want, but it's not executed when shutting down. And, just as a fun fact, same script and configuration on a raspberry pi works just as expected.

You guys are the experts... anybody any idea?

PS: uname -a output:

Linux d3bi4n 3.16.0-4-amd64 #1 SMP Debian 3.16.7-2 (2014-11-06) x86_64 GNU/Linux