One solution to OP's problem is to strengthen libel and slander laws to deter people from casually publishing fraudulent news, akin to a DMCA takedown request b

One solution to OP's problem is to strengthen libel and slander laws to deter people from casually publishing fraudulent news, akin to a DMCA takedown request but perhaps a bit more bite. In this case I would distinguish publishing from 'sharing' with a bit more legal finesse. The problem is the press will scream bloody murder at any attempt to reign in their right to publish, perhaps rightfully so. IANAL.