What they teach undergrads about the experiment: People blindly follow orders. If the Nazis ordered you to commit atrocities, you probably would!
What the experiment actually showed: People follow orders when the orders are justified within a persuasive ideological context, e.g. you value science and the scientific researcher is telling you to proceed for the sake of science.
In the first, people who follow the orders of Nazis are not necessarily ideologically aligned with the Nazis, they might just be in a brainless order-following trance. But this isn't real, and in reality the people who were "just following orders" were in fact ideological committed to the cause and should be judged accordingly.