You’re correct that the messenger does not change the truth of the message, but in this particular instance, they’re also simply incorrect irrelevant of their sincerity. They say that no one believes a thing and they got downvoted. That itself shows that in all likelihood most people who have seen the comment disagree, suggesting that at least some believe it. The only way to defend the statement is to try to argue that those people don’t count, which would be special pleading.