Edit: Yes, I am very aware both parties should then be considered morally responsible.
Usually, the general use of language tries to hide this. Presidents "order killings", and people "pull the trigger, but the orders come from elsewhere". Nobody involved feels like a murderer, opposed to all of them.
That's generally because of laws which explicitly make procuring, soliciting, etc., a crime that is actually committed an offense for which the perpetrator can be punished as a principal of the solicited, procured, etc., offense; that is, the law recognizes that the acts involved is meaningfully distinct, but assigns the same culpability to those distinct acts.
So, the analogy to law sort of undermines the idea posited upthread that it doesn't make sense to distinguish the act of authorizing from the act of performing what has been authorized.
Unfortunately, we can't accurately test it _yet_. A huge amount of data and tests -along with massive improvements in the understanding of the human brain- would be required to make a complete snapshot, without which testing isn't possible. We can't eve be sure this theoretical test is possible.
This alone wouldn't prove that their hands are clean, just that they wouldn't be as much to blame as someone who didn't succumb to social pressures and had more of a choice in the matter.
I don't think this is the real deal behind that decision. We've established that people are generally pretty susceptible to authority and peer pressure. Moreover, military training exists primarily to increase it. But the effect that legal clause has is that it counteracts this susceptibility by removing any doubt you could have that you'll be on the hook if you follow orders telling you to commit atrocities. It reduces the effect of peer pressure.