This happens because you are using an old version of WordPress and the Recent Posts widget. Remove the widget or update your blogging software.
I had the same problem. Even with the newest version of WordPress, the WordPress.com Stats plugin won’t work correctly if you use the Recent Posts widget. That’s a shame.
Also, if you are using the K2 theme you must use Widgets instead of the Side Bar Manager that the theme comes with. Also a shame.
But stats are working now and I suppose it’s worth the compromise.
Are you using the latest version of the wordpress.com stats plugin? That would be version 1.1.1, available here:
http://wordpress.org/extend/plugins/stats/
I see the potential issue you’re talking about, but as far as I can tell it avoids that issue because it’s using $wp_the_query, which always holds the default query. The Recent Posts widget creates a new query, not modifying the existing one. So it should work correctly with the latest WordPress and the latest stats plugin.