Note that in the Milgram experiment the scientist figure never tells the subject it's safe or makes excuses for the degree of shock administered, they just insist that an external authority 'the experiment' requires the subject to continue.
The researcher tells you to keep going, and that the shocks will cause "no permanent tissue damage" to the Learner.
The disturbing issue raised by Milgram's experiment is how you can apparently persuade a majority of people to do just about anything, as long you have an appropriate authority figure around to affirm that it's safe/ legal/ necessary. With things like waterboarding and suicide bombing being stples of the news in recent years, this strikes me as a serious problem.
If this is the case, it seems that he improvised rationalizations as needed to get the subjects to continue administering shocks. This strikes me as rather sloppy on his part. (...not that I think the numbers would have been all that different had he not done this.)
Second, I think the "(65% of) people obey to authority despite what should be their better judgment" overfits the results of the experiment. Perhaps people simply listen to scientists during experiments?