http://www.abc.net.au/radionational/programs/radioeye/beyond-the-shock-machine/3183356 
I’m also author of the book ‘Behind the shock machine. The untold story of the notorious Milgram psychology experiments.’  

Milgram said, in response to claims that his subjects knew it was fake, “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.”

One of the reasons these experiments aren’t repeated much any more is because they have profound, sometimes permanent effects on the “shockers” which is an ethical violation of the first order – a violation of the Hippocratic Oath and all that stuff.

“She investigates Milgram’s character and motivations, revealing him to be perhaps a little too invested in the results going the way they did. She uncovers some evidence contrary to Milgram’s reported findings that he, unsurprisingly, never published. She tracks down previous participants to ask a particularly difficult question – were the psychological effects of the experiment really as ‘negligible’ as Milgram claimed? And she casts some doubt as to whether the experiment really was measuring ‘obedience to authority’.”
TL;DR ~ More than a 3rd of the test subjects new the actor wasn’t getting zapped

So the shocker only has a moral choice to make if they become convinced the shockie is under coercion.  In that circumstance the shocker is under implied coercion since this is not what they originally agreed to.  Backed up by the article  “I didn’t know what was going to happen to me if I stopped. He just—he had no emotion. I was afraid of him.”

This contradicts the most common cultural reference to the experiments, which is usually trotted out to justify the “I was just following orders” defense. When you feel that the choice is being taken away from you, you are least likely to acquiesce. Conversely, it follows that the decision you make is of your own volition. This is a fairly profound finding when considered in light of guilt or innocence and Milgram has often come up in war crimes trials (the fact that it’s easy to mischaracterize leads it to be used by both sides…). 

But you’re right; follow-up on the experimental subjects is particularly interesting.

(Experimentation also showed that the compliance rate went up greatly when peer pressure was added, for example.  Experiments 17 and 18 in the initial Milgram set are particularly interesting in this regard.)

I recall giggling in response to the screams

Yes, but did the fake screams sound funny?

If the person receiving the shocks can’t escape of their own volition why should the person delivering the shocks believe they have any option  but compliance either – the person receiving the shocks has far more reason to call a halt to the whole thing and yet hasn’t.

Complete with inappropriate laughter, in some instances.

Could it be that they knew it was fake?

Not all Milgrim’s results were discouraging.  If the subject is paired with another person and they share the task of supposedly delivering shocks, and that other person resists the command to deliver a shock, the subject is much less likely to deliver the shock as well.  So resistance to authority may make it easier for others to summon the courage to do the same.

The actual conclusions were not that we blindly respond to authority (we don’ t), but that we will do seemingly terrible and irrational things of our own accord, if we can be convinced that it is the right thing to do, or is in service to a greater good.

I don’t recall Milgram saying that in any of his papers.  He said that many of us will commit atrocities if we can be persuaded that we are being ordered to do so by a “legitimate authority figure” – not that we believe this explicitly serves any greater good.  The key seems to be that we believe the person we are obeying has some sort of right to command us, within our framework of authority.  The uniform of a clipboard and white lab coat convinces a startling number of people.

http://www.typinganimal.net/wp/stanley-milgrams-experiment/ is another brief look at the subject.

If something really does “bother you” about the Milgram experiments, I suggest you do some more research to see if the study itself might answer your question, or possibly the commentary on the research. Its only, like, the most studied and referenced social psych experiment ever.

Shermer gets a failing grade for this and I hope SA’s readership makes that clear.