Caveat: I haven't read the book Cory's referencing. However, the allegations he mentions are not new, and when I studied the matter extensively years ago I found them very unconvincing, to say the least.
I will give you Milgram's own response: "Orne's suggestion that the subjects only feigned sweating, trembling, and stuttering to please the experimenter is pathetically detached from reality, equivalent to the statement that hemophiliacs bleed to keep their physicians busy." (1972)
Milgram's experiment is repeatable and has been repeated.