Facebook isn't concerned about fake news, it's concerned about bad press and possibly facing regulation. Make the bad press about Facebook fake news go away and Facebook will stop caring about fake news on their platform.
I'm not saying FB's concern is sincere, just that it exists. They are aware there's an issue. They are aware it could hurt them.
Jeff \ Amazon seem to be taking the head in the sand approach.
They are both equally "concerned". They can see their metrics and they know when bad reputation is hurting more than increased hits/throughput is helping