Your “truth” is an inference that you are drawing based on circumstantial evidence that contradicts the witness’s story. Even if I agree with you that conclusion is probably correct, in US law we would treat that as a “disputed fact” that would require a jury to resolve.
I think Facebook shouldn’t moderate political content, full stop, but if it did, surely the limit is things that provably false without making judgment calls or evaluating credibility. E.g. “Hilary Clinton was indicted for her emails but Obama pardoned her.” It’s shocking to me that anyone would espouse Facebook making editorial decisions on political ads based on inferences from the evidence that in a court of law a judge wouldn’t be empowered to make.
And if Facebook moderators should be able to make inferences and weigh credibility in deciding “truth” doesn’t that circle back to my point about education spending? The US spends more on education than all but 1-2 other OECD countries. Can’t a moderator infer from that the assertion that schools are underfunded is false?