Happily from the sidelines - it probably is fraud and this isn't really an article targeted at the general audience. But the statistical evidence proves beyond a doubt that the data wasn't collected by the methods described in the paper. That doesn't prove it is fraudulent because formally speaking he can't rule out that they just did a very bad job of explaining their methods.
Just from life experience, any time anyone goes in guns blazing based on statistical evidence - without actually talking to the people involved - it is often a mistake. Just because someone can't think of an alternative reason says more about their imagination than the reality of the situation. Particularly coming in hot off a twitter argument.
That being said, these are unusual and unexpected patterns that show irregularities in the data, and I would certainly share his concerns.