If that's your concern, fine. Then just ask for evidence for the lie. That takes 10 seconds, and costs the liar the 10 minutes. Don't just say "you're wrong". Even if they are in fact wrong, it's still really weak. People aren't going to believe you. (Nor should they, based on what you've presented, which is nothing but a bare denial.)

I agree that the original claimant has the burden of proof. But this isn't high school debate. The people reading your posts aren't debate judges (for the most part), they're just people. They aren't (for the most part) going to apply strict debate judging rules to the exchange. And if all you say is "is not!", to people reading the exchange, you look like you have no evidence and therefore have fallen back to arguing like a five-year-old. It's not a convincing look, even if you're right, and even if the other side actually has the burden of proof.