Button is way too simplistic. A form where you could state your proof along with other arguments why a news is untruthful or otherwise overly antagonizing would

Button is way too simplistic. A form where you could state your proof along with other arguments why a news is untruthful or otherwise overly antagonizing would work better, but would be hard to evaluate by automatic means. Maybe after a certain threshold have been reached and the complaints vetted by a human, you could start removing the news or even blocking the news site from being shared on Facebook. Most likely the system would be gamed to attempt to block major sites like CNN, but would work well for smaller, dubious sites that have no real other purpose than creating provoking news.