It might be arbitrary, but it doesn’t have to be. You can measure the human perception of indirection. The trolley proplem has a different answer if you order someone to pull the lever instead of pulling the lever your self. The Milgram experiment only works if there is at least one level of indirection, and works better the more levels there are.

I would guess an expert anthropologist would know about this cognitive effect and count for it.

I take your point, but citing Milgram is a bad idea. The Milgram experiment turns out not to work that well at all, or at best to require very specific sort of conditions to get people to behave as they did for his iteration.

Regardless of the conclusion, the experiments are robust and show that people behave differently with different levels of indirection. So the experiments can still be used to argue that the effects of indirection are real and probably measurable.