The problem is much more difficult than creating a classifier. The purpose of filtering news is to control the impact, not to control the tactic. The last time Facebook issued a surge to control 'spam' posts for the same government concerns they seek to deal with "fake news" today, they took out pro-Sanders articles, censored sharing of the Snowden documents, prevented people from linking to Wikileaks, and shut down Facebook organizing for May Day protests.

Facebook regularly censors and directs conversation online around the world to the whims of various regimes and administrations, but it's just not easy "use machine learning".

The issue is that machine learning is inherently modeled to solve decision problems in spaces that separate high level 'features' from low level observations. The study and practice of machine learning thus far has modeled noise, uncertainty and complex state spaces.

However, machine learning classifiers do not themselves have a concept of adversarial data: this led, for example, to spammers who would "poison" machine learning classifiers by biasing them to learn the wrong things, so that they could get their spam through. Similarly, not too long ago, Microsoft put a conversation bot on the web that 'learned the wrong things' because people approached the bot in an attempt to trick it.

Facebook's requirement for battling unsanctioned opinions is that it solves this problem - it hasn't been solved yet. Facebook needs to continuously monitor the adapting activity and patterns of people who are trying to say things that governments and Facebook customers don't want people saying.

Basically: machine learning doesn't adapt but people do, and naive attempts to get machine learning to adapt make it vulnerable to being tricked, because classifier theory inherently has no concept of adversarial data.