Twitter, by default, uses Bit.ly to shorten URLs for use with SMS, the API, etc. But on its Web site Twitter shows you the original URL (or at least part of it) so that people know where they'll be going if they click on the link. Or, at least that is why I think they are doing it. If they were to keep the Bit.ly URL then people wouldn't know what will happen if they click on the link.
However, this causes some problems when trying to copy/paste a tweet. See the screenshot of this tweet.
If you try to copy/paste that Tweet you'll end up getting an unusable URL. Perhaps Twitter should throw the 140 character limit out of the window on the tweet permalinks to make the full URL visible. This would make it easier to copy/paste but also simple to see whether or not the URL you are clicking on will lead to a Web page, a PDF file, an MP3 file, etc.