If there’s actual, provable lies about a notable person in the encyclopedia, then there should be actual, provable truths to combat it
No, not necessarily. Lots of false info spreads around, including serious academic publications. People who publish books and articles don't always do additional verification of the stuff they read elsewhere. And if nobody publishes something containing the correct version of the story, you as a WP editor don't really have a reliable source that you can use against the existing ones. I've seen this happen multiple times. Wikipedia is nominally meant just to convey what the sources say, not do active research or provide you with the capital T Truth.