The author's lack of mathematical literacy is pretty striking. I don't mean not realizing it was a log ratio, but presenting the raw percentage-to-pixel expression as if it were meaningful. Clearly the constant term and overall scale factor just depend on the basic dimensions of the plot, so ultimately the mapping they found is x-0.21x^2.

Beyond that, they were just picking a hypothesis without thinking how a bad plot could have been generated. It's interesting to note that the correct mapping, from their perspective, would have been the Taylor expansion of log(1+x), which would start x-x^2/2+x^3/3, so their goodness of fit metric (large R^2) wasn't a useful indicator, and there wasn't a meaningful place to cut off the degree.