The claim made by the OP is "if people believe in what they're doing, they will hurt people;" the claim made by nigerweiss is "if people use system 1 thinking, they will hurt people." To differentiate between them, we need a statement intended to make people use system 1 thinking without relying on them believing what they are doing.
It's not clear to me that nigerweiss's division is more precise than the OP's division, or has significant predictive accuracy. I would have expected "you have no other choice" to evoke 'keep your head down, do what you're told, they must know what they're doing'; that is, the system 1 thinking that nigerweiss claims would lead people to push the button, when it led to less people pushing the button. Why is it a status attack that awakens system 2 (huh?), except because we know what we need to predict?
Here is a paper in PLOS Biology re-considering the lessons of some classic psychology experiments invoked here often (via).
Contesting the “Nature” Of Conformity: What Milgram and Zimbardo's Studies Really Show
To me the crux of the paper comes from this statement in the abstract:
Plus this detail from the Milgram experiment: