For all intents and purposes they should be responsible for everything that happens on the platform regardless of where the content was picked up from. They should have a responsibility but this comes in conflict with their goal to to drive engagement and profits.
Their algorithm curates what people see, shows specific links, and influences opinions. And when you can influence opinions on such a large scale and monetize it we have a conflict of interest and even a weapon. FB and others have proven this in the past. Why do you think the media is regulated so tightly around election time? FB can take even a blog post and push it so aggressively right before elections that they manage to sway opinions but still claim they were just a platform.
Let's put it in terms other than politics...
In the early 1980s a full third of all households in the US watched the TV show "Dallas" every weekend. Was "Dallas" the greatest performance ever made or just the best option out of 3 choices?
They are a platform rather than a publisher, in my view at least.