I ran into this problem. I got an error with WordPress.com Stats plugin. It was just a message but it looked ugly and although I had already installed API key and was getting stats, I wanted to remove it. Here is what I did.

I went into the database using phpmyadmin from my cPanel (your hosting may or may not have phpmyadmin, so you may want to edit the database some other way). I suggest you to backup your database, just in case you mess up.

Browse the wp_options table and locate stats_options. The value should look something like this:
a:7:{s:4:"host";s:16:"yourblogurl.tld/path";s:4:"path";s:1:"/";
s:7:"blog_id";i:blog_id_numeric;s:7:"version";s:1:"3";s:5:"error";
b:0;s:9:"key_check";b:0;s:7:"api_key";N;}

Then edit it and change the value to null (i.e. delete the contents and leave it blank). Now, go to admin area of your blog and add the API key.