Some of the teachers undoubtedly thought it was fake, others did not. And importantly a majority of the teachers were not properly debriefed until several months later (some never were). The "dehoaxing" most received immediately following the experiment was itself another hoax which in some cases was meant to persuade the teacher they had in fact been shocking somebody (but that the shocks were only very slight harmless shocks.) The dehoaxing was meant to introduce the teachers to the learner, to demonstrate that he was alive. Some did not even receive this dehoaxing, presumably because procedure was violated, which explains why a handful of them might believe they'd killed somebody.
No. No. No. That is entirely wrong. Watch the original video. Every one of the teachers is introduced to the learner after the experiment and they were told no actual harm came to them. At least in the original Milgram iteration, all of the teachers knew by the end.
[1] https://www.amazon.com/Behind-Shock-Machine-psychology-exper...
[2] Funny anecdote- when I was still in science (brain imaging) a reporter from a major news outlet interviewed another member of my lab about what brain activity would look like in a dead person's brain. The question was entirely serious.
https://www.independent.co.uk/news/science/what-happens-die-...
You too are being slightly too generous towards scientific journalism- a typical non-scientific audience wouldn't make the distinction between clinical and brain death, and the reporter likely wasn't either.
>...with all the work they put in at Harvard
I think the experiments were done at Yale.
Milgram wrote a book about the experiments and I agree, (at least as described in his book), they worked hard to test the hypothesis. (Setting up experiments outside the university, using both male and female experimenters, Having the experimenter play the student, etc.)
https://www.amazon.com/Obedience-Authority-Experimental-Pere...
Not to mention his experiment was replicated by several universities around the world[1], although due to modern ethical standards, it would be impossible to reproduce ethically at most universities today[2].
I don't think Milgram falls into the same category, especially with all the work they put in at Harvard in the controls (the learner was a tape recording; so everyone heard the exact same thing. It was the same professor in the room with him; always replicating the same dialog).
This is in direct contrast with Vsauce's trolley problem experiment, which had way too small a sample size, and who forced a response for one person by changing the conditions of the experiment (there was no one outside when he tried to get help).
[1]: https://en.wikipedia.org/wiki/Milgram_experiment#Replication...
[2]: https://www.psychologicalscience.org/observer/replicating-mi...