I'm not really concerned what others are saying. You made the claim that "There's no reason for my health to be harmed just because someone has more than me." I just gave an intuitive explanation of how this could happen. And you can see this happening on a global scale: wealthy countries attract more higher-skilled workers, like doctors. These are educated, capable people not contributing those skills to their home countries (to be clear, I wholeheartedly support open immigration policies, but that doesn't mean "brain drain" isn't real).
EDIT: ah, I was not reading carefully, and realize you are saying "I see no reason for my health to be harmed by the sole fact of being poorer than someone else." I am not familiar with Sapolsky's research and can't speculate. In principle, I do see why you'd think it's hard to disentangle the material impacts of inequality from the psychological.