Anyone experiencing major issues with the Stats plugin authenticating with WordPress.com (in particular, WP.com coming up with an error similar to “you do not have sufficient permissions to access this page”) should be advised that it appears to have been deprecated as a standalone plugin.
The majority of Automattic’s offerings, bar Akismet, have been assimilated into the new Jetpack plugin, which promises better integration and more frequent updates to closer track to the WordPress.com state of affairs. Features for your site that you don’t want for your site can easily be disabled, and setup is extremely straightforward.
My only complaint is that it would’ve been nicer for Automattic to provide an indication in the old Stats plugin’s access panel that those of us still using it needed to download Jetpack for future updates.