That hypothetical score will just trend towards 50% as people who disagree with the slant of the story (or more realistically, the source, since people even here make knee-jerk judgments based on source without even reading the meat of the story) will vote it down and those who agree vote it up.

I am not suggesting a democratic end-user process, I am suggesting making the investment of a fact-checking department that any credible news source would be delighted to fund and create. The end-user process is the sharing, the veracity metric must be up-stream, or something that is triggered once a threshold number of users start sharing/approving something. To know the veracity of something that "goes viral" would be valuable, and the veracity metric is not something that end-users would be able to edit directly.

My thought would be that it would be at the source level. "98% of people find this source reliable", though that's certainly subject to the same biases.

Better systems might require more work to mark a story as false (such as how reporting a story as false currently works in Facebook.) Over time, Facebook can see on their end which domains are pushing fake news and choose not to surface unreliable sources on people's news feeds.

That idea is also vulnerable. Conservatives will just flag off stories from MSNBC, liberals will just flag off stories from Brietbart, the truth of the actual article notwithstanding.