The issue in my opinion is that there are various, almost-equally "true" perspectives that can be reenforced with facts and presented. That there is no single objective truth to all matters means that biases (political, religious, etc.) act as a lens and the "truth" presented on fact-checking sites (and elsewhere) is shaped by this lens. This is why you can have news organizations with different political slants painting a story two entirely different ways, without directly lying.