https://phys.org/news/2017-08-mozilla-fact-checker-fake-news...
(Apologies for the awful link source, I can't find a primary AFP link. Several other sites that have published the same identical story.)
Full Fact does appear to be a real organization, they claim to already work with the BBC, Guardian & other media partners, as well as Google. Some of the controversy seems to be over their grant funding from Omidyar Network and an organization founded by George Soros. (Whether that's a reason for concern, I have no idea.)
https://fullfact.org/blog/2017/jun/automated-fact-checking-f...
https://fullfact.org/blog/2017/jun/awarded-500000-omidyar-ne...
https://www.theguardian.com/technology/2017/aug/08/fake-news...
Edit: Misread, thought OP was talking about Google not Mozilla.