Lots of people tweet. Lots of famous, newsworthy people tweet. What people tweet--whether those people are famous or not--is not newsworthy.
This problem is worst, probably, in sportswriting. There's always material for journalists, because many athletes tweet, and many athletes are idiots, and famous people with no filter apparently have a massive hold on our collective imagination.
But it is not journalism to trawl Twitter and see that Lance Armstrong was cranky about something for the five seconds it took to tweet about it. That is not news--literally or figuratively. It is not news to blow up the Brandi Chastain vs. Hope Solo spat into a major sports story, because there's no there there. Sure, it's public, but there is no substance to it, either in the production or the harvesting.
So people are twits on Twitter. Let's not give them a bigger platform.