The "all claims are facts unless proven otherwise" is a wrong way to think about. You must prove a claim, not the other way around. What is perhaps better to say is that he makes no arguments but just lists observations (nitpick: therefore can be no such thing as rebuttal). As the commentary tweets don't call them wrong, we can assume they're indeed correct (thus nothing was debunked). That said, I'ld have preferred if he had correct citations such as the link to the Nature article.