I believe the article the OP points to is actually more about how system 2 is being engaged in these systems, and is therefore not "blind obedience", i.e. a simple heuristic being engaged. From the conclusion:

On the other hand, it ignores the evidence that those who do heed authority in doing evil do so knowingly not blindly, >actively not passively, creatively not automatically. They do so out of belief not by nature, out of choice not by necessity. >In short, they should be seen—and judged—as engaged followers not as blind conformists

Equally, what is shocking about Milgram's experiments is that rather than being distressed by their actions, participants >could be led to construe them as “service” in the cause of “goodness.”

At root, the fundamental point is that tyranny does not flourish because perpetrators are helpless and ignorant of their >actions. It flourishes because they actively identify with those who promote vicious acts as virtuous [49]. It is this >conviction that steels participants to do their dirty work and that makes them work energetically and creatively to ensure >its success. Moreover, this work is something for which they actively wish to be held accountable—so long as it secures >the approbation of those in power.

To put words into their mouth, I believe they are arguing that people's system 2's are overriding the "don't hurt people" heuristic of system 1, as opposed to system 2 analysis being overridden by a simple obedience heuristic.