They go on to give supporting analysis in form of the false positive and false negative rates by race, which is pretty compelling evidence. You claim to not believe that because you cant find it in the notebook but its literally right underneath the Cox model section.
I was intrigued by this article and went a step further to plot the ROC curves and the evidence is solid. It's messy, but you can see it here https://github.com/stoddardg/compas-analysis/blob/master/my_... in cell 78. Its quite clear that the algorithm is choosing a different point of optimization on the ROC for white people (a more lenient one) than for black people. A white defendant with a risk score of 5 is as likely to commit a crime as a black defendant is with a score of 7. That's an obvious case where you could simply relabel and be more fair but their algorithm chooses not to.
I also hate when people abuse bad statistics and reasoning to sell page views.