I definitely wouldn't go off a single person that I didn't know personally's Tweets, usually on anything of consequence you would look for multiple confirmations on Twitter and some evidence of the event in other places online.
You though, lacking superpowers, couldn't help if you were there. So I dunno, maybe you should frantically search until you get positive evidence, and an idea of what you could do to help, before you decide what to do.
There are laws to deal with the guy if these was a scheme to profit. If he was deluded there's no reason to take actions, he's no worse than the idiots who ran around because of his rumors. In fact his action was better. By forwarding his news he's inviting conversation and investigation, by running off to the school the terrified parents are actually potentially causing a problem.