Well, for a start we'd need some form of fact checking that was actually about just the facts rather than political spin, and that's really hard to do once politics becomes involved. Even purely factual questions like whether someone said something or not become blurry.
For example, take the child rape trial Hillary Clinton was a defence attorney for, in which she claimed that an unspecified person had told her the victim "is emotionally unstable with a tendency to seek out older men and to engage in fantasizing" and "has in the past made false accusations" to justify putting her through a nasty court-ordered psychiatric exam. Is this the same as Hillary herself making the claims? The original viral version and the victim saw it this way. Snopes argued that this was a lie because the document showed that other people had made the claims, neglecting to mention that the interpretation and wording was Hillary's and the existence and honesty of these other people rested entirely on her word. Neither of these is inherently more truthful than the other, it's a question of which spin is politically convenient.
This is probably the most clear-cut example imaginable too, since it's about the contents of a court filing. Most of the world is a lot more factually unclear, visible only through a lens of conflicting evidence and multiple sources of information.