Not all people who use the twitter back end come from the Twitter websites. I notice quite a few tweetdeck users here in GFY. Many twitters also use their phones. This article from EasyTweet's blog describes the issue of twitter source traffic accuracy and how to use Google Analytics to track non-Twitter website twitter traffic.
Source:
Easy Tweet
Resource:
http://blog.easytweets.com/how-to-tr...gle-analytics/