Correlation very much implies causation, it just doesn't guarantee it. After you test that hypothesis, you'd find correlation if the hypothesis was correct. Saying "correlation is not causation" is useful for dismissing data offhand, but where you find causation you'll find correlation.

Also, graphs are demonstrably NOT completely meaningless. They can absolutely be misleading, but they can also accurately depict the underlying data. I think the point of this thread is that the authors of this study have proposed a hypothesis and collected data that supposedly reinforces it. The data (and methodology) can be analysed and verified. There's no need to start from scratch, in this case, to determine if the findings can be substantiated.