Once upon a time it was possible to get a clean (not rel=nofollow) link from one's Twitter profile: http://www.davidnaylor.co.uk/twitter-backlink-tip.html

Presumably for anti-spam reasons, Matt Cutts (of Google, and regular Hacker News commenter) implied in a tweet that Twitter would want to fix this: https://twitter.com/mattcutts/statuses/865610396

I think this implies - in my opinion rightly - that Google want or wanted links on Twitter to have the nofollow attribute set.