I personally am for removing any tweet that doesn't come from a credible source. And ban the offender if they keep on doing it.
The trust me bro tweets, like the whackjob explaining why it was an israeli rocket that hit the hospital, need to disappear (we'll probably never know what really happened, although I think that for once the IDF wasn't behind it). Also those showing acts of extreme violence, like a kid or a woman being shot. The latter are just obscene, unhealthy, fuel the rage and don't help in any way the discussion.