The problem is that, while it’s easily disproven, the majority of people who read his statement will take it at face value, and because his platform is so large, it would take a lot of people disproving his claim to have even a fraction of the same reach.

People with appreciably large platforms or loud microphones can spread disinformation with no recourse, and there’s really no effective way to counter it. I don’t know what the solution to this is, but it’s a huge problem and has been for quite some time.