[MarkusQ]

Yeah. And that's really important; If someone makes a correct claim by accident, say they misread a paper that incorrectly claims X as correctly claiming not-X, we shouldn't consider it evidence that they are trustworthy or honest, just lucky.

But then you have cases where someone correctly cites a source that they know to be incorrect (or at least plausibly should know). This is commonly done when flawed studies are funded specifically so they can be cited. This is arguably even more egregious lying, yet would pass a consistency based "fact check".

Likewise, the factual claim ("eight out of ten doctors surveyed recommend smoking brand-x") can be true while the implication is false.

In short, I'm not claiming such checks can't catch liars (they can), just that passing such checks doesn't mean they were telling the truth or what they said or implied was correct.