In Sociolution terms, a fact is an Atomic, Unambiguous and Indisputable building block which can serve as a solid foundation for unbiased, unencumbered, logical reasoning. As per Sociolution's definition, if there is any room for disagreement about the accuracy or correctness of a factual assertion, then it is not to be classified as a fact. On the other hand, facts that leave no room for disagreement can be used to draw complex, logically coherent conclusions, on which even more complex conclusions can be drawn. This concept is one of the cornerstones of Sociolution.
Today's fact-checkers are predominantly sponsored by wealthy and influential organisations, created to promote personal agendas or political narratives. The world of politics is very complex, and it is a messy one. There are normally deep disagreements about the facts themselves, and the truth as stated is often of a very subjective nature. Politically motivated, cognitive biases are arguably the biggest problem we are seeing in today's fack-checkers.
Many fact-checks assess more than one claim, and the claims are often ambiguous, which is not surprising due to the inherently ambiguous nature of natural language. Further to that, more commonly than not, a series of fact are deemed to be false simply because one of the facts is deemed to be false. This is very problematic, especially when the verdict is based on flawed logic or the lack of credible sources.
Needless to say, a fact-check based on claims that are not backed up with at least one reliable source is of little value. But we see this sort of thing occurring all the time.
Even in the most credible fact-checkers (credible by name, not by merits), there is a clear tendency towards flawed or incomplete logic, rendering the validity of the fact-check null and void.