The real problem here is that people put trust in things they should be skeptic about and the official certification not only doesn't fix it, actually it could make it worse depending on who is in power...
Anyway, accreditation would make it even more troublesome and still would not solve the root issue and even if we focus on scenario OP described: FB ranking the news by trust, there are still many loopholes here. Like publishing true news with a spin or simply spamming worthless articles "Random Celebrity said good things about President Candidate" - just that alone would still do the trick.
That said, Facebook could be better with very small updates to catch paid propaganda.
I am Swedish, a country with a small population close to Russia. On public people's open FB accounts you will often find a lot of comments with very unusual opinions in Sweden, writing exactly the same thing as Putin's media.
The way to identify these accounts is to see if they can write anything negative about Putin. I typically write: "Do you condemn Putin for starting wars for territory in Europe again, like Hitler and Stalin in the 30s?". If they can't, it is overwhelmingly likely that is someone working in St Petersburg -- even most Swedish old style communists get upset by that.
Sorry for the rant, this is irritating.
Edit: On second consideration, it was quite a while since I saw these accounts? Maybe FB started doing exactly that.
Governments license news organizations and journalists. Governments review stories. Governments run the legal print and broadcast media. Governments regulate access to web sites.
Be careful what you ask for...but consider donating to Poynter: http://www.poynter.org/
What about a browser extension that allows users to "rate" each story/author?
You could follow other users you trust, and get an aggregate of their ratings so you wouldn't just get the global rating, which could be corrupted.