Today saw this eventually delivered; in perfect timing for a lazy Sundaypic.twitter.com/Hq9KvOkiTd
You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more
My first impressions of it suggest that you're absolutely right
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.