Ok, I figured out the issue in my case.
It looks like the wp.me link is generated when installing the WordPress Stats add-on. Which means that the error occurs when you install the add-on on both domains.
So a warning for everybody installing dev areas by copying their live areas: DO NOT, DO NOT, DO NOT COPY ALSO THE WORDPRESS STATS PLUGIN WITH THE API KEY.
Google will penalize you – the latest algorithm seems to be overzealous about this. We have lost 66% of traffic for content duplication.
On a note for less technical users, this is NOT a link you can see by simply visiting a page; it is added to the Headers sent with each request to your blog. Googlebot will fetch this value and use it.
Now, I need to figure out why wp.me is linking to our subdomain.
Ah thank you. Beautifully customized looks.