To the great shame of the human race, it's not about truth or lie. It's about what a person thinks first. Like, literally, if you don't have an opinion on something, and then you hear about it, and the first thing you think is, "That sounds reasonable," then that's a big wall to overcome if that information is wrong.
And after that is even worse, because then you already have an opinion, and confirmation bias kicks in. So, everything seems to support that opinion.
And that, of course, is one reason why conservatives are so against public schools, and especially against them teaching anything verifiable like science or accurate history. A school has the chance to counter the parents' indoctrination because the children are still young.