Milgram was full of crap. He neglected to include in his publications the fact that the people who went all the way in the experiment didn't actually believe the other person was real. The ones who did believe he was real were the ones who stopped the experiment. Effectively, the conclusions for the experiment were the opposite of what they should have been.
It was the same kind of experimental/reporting bias as for the famous Stanford prison experiment, where 'prison guards' were shown to act in cruel and depraved ways towards 'prisoners'. The researchers in that case actively encouraged the 'guards' to act that way. That makes the conclusions completely unsupportable.