Your examples do not mean much when it comes to actual influence and its use. Google relies on blatantly left-leaning "fact checkers", Schmidt was very active in HRC's campaign, Twitter actively censors Right-leaning hashtags and users [1], Facebook censor(s/ed) conservatives [2]. Do you really think actual censorship and suppression (when claiming otherwise and pretending to be objective) is less important than letting Trump takes questions?
There's no such thing as agnostic fact checkers. Facts are complicated by context and anyone who claims to objectively "check" them is selling you snake oil. For example, the lead Snopes fact-checker was previously a liberal blogger. Guess which way their fact-checking skews?
We're all human and we have our biases, whether we like it or not. It doesn't take much effort to tweak an assertion to go from "Mostly false" to "mostly true" - it just depends on which one the writer favors. My BS detector goes haywire whenever someone claims to offer non-subjective anything. tl;dr investigate facts and claims yourself and never trust those who have power over you, even if you vote for them!
[1] http://thehill.com/blogs/pundits-blog/media/303295-how-faceb...
[2] http://gizmodo.com/former-facebook-workers-we-routinely-supp...