The media now has Twitter too, so it is easy to run a story on anything by saying it's being reported on Twitter.
It seems the media now assumes that it's fine to report what someone else has said in the same way as a properly researched/verified story, but if proven wrong, simply point out that it was only from Twitter, so what did anyone expect? As ChrisCooper says, for the online/TV sites you simply delete the story and never mention it again!
How many stories have you heard about late at night (or through the night) that you thought you'd find out more about in the morning, then it's gone. Did you dream it? Well, maybe, as unless Google still has it cached, it's history. Naturally, you can't easily show how often this happens as the stories are gone (or edited heavily, such that Google now replaces the incorrect copy with something else and helps hide the mistake).
Online has really helped lazy journalists, who can now write something now and then add to the story (or correct it) later. It also makes it easy to write stuff that can be deleted completely, even including material that could land a publisher in deep trouble if put into print - but where lawyers might be content to simply have the online story removed.
But, despite this, I think the media do know how to read between the lines on certain things and report accurately more often than not, even before getting the official confirmation.