I wish the article said more. It is hard not to see anything 140 characters or less as fair use.
They're talking about links to infringing content (people tweeting file locker links for movies/games) and stuff like people posting photos they don't own.
This user (@mikko) has one of his tweets 'withheld' and the content of the tweet is changed to the withheld notice, but his followers can't work out whether the note is from Twitter or @mikko himself.
I appreciate text has its uses as a lowest common denominator means of communication, but it also has its drawbacks...