The gist of the article is that statistical bias is not the bias that journalists are interested in. The article doesn't discuss how these biases are related or relevant to each other, but rather assumes that statistical bias is the only one that should matter. I think the article is missing a discussion of the gaps between what are the measured inputs into your statistical model, and what can be acted upon from a policy perspective.
As a thought experiment, suppose the only two inputs that determine a person's recidivism rate is their past criminal history and whether they had lead poisoning as a child, but that of these two we can only measure past criminal history as an input into our algorithm. If race is strongly associated with childhood lead poisoning (such as in real life [1]), then our algorithm might get higher classification accuracy by including race [2] as an input in its training data. This might have less statistical bias, but would bias against individuals of a race who are in truth not at higher risk of recidivism.
[1] https://scholar.harvard.edu/files/alixwinter/files/sampson_w...
[2] The actual COMPAS algorithm doesn't use race as an explicit input, but that doesn't really change the issue.