Hey Karlatzke, just had the same problem and solved it.
When you install the stats plugin, it writes a couple of lines in the footer: <script src=”https://stats.wordpress.com…
So first I added <?php wp_footer(); ?> which stands just before the </body>, then I made footer.php writable and then I reinstalled the plugin. Now it works! You will see the stats.wordpress.com script in your pages source only if you’re not logged in into wordpress!