I cannot comment on the specific point raised here, it’s been a while since I read Milgram’s book, but I remember that many different experimental conditions have been tested, and I don’t think that picking out a single one of them and reinterpreting some minute aspect changes the overall significance.
Moreover, if you’re in the sorry situation of being on the receiving end of some punishment ordered by an authority figure, like the “learner” in the experiment, does it really matter that whoever doles out the punishment, does so not because of an explicit order but because he is being coaxed in various ways to obey?
One key point of the experiments is that the overseer has no formal authority over the teacher at all, and the fact that a lab coat and some easy psychological conditioning steps are sufficient to make over half of the population obey should give anyone food for thought.
Skipping a few steps of thought here, but my conclusion is that we are all being groomed to obey authority figures – the “con” aspect is not decoupled from that; it is one of many mechanisms that are used to exert control. What Milgram showed is a practical consequence of that process.