I too have an orchard of 15 trees and the chickens eat their fill of apples as often as they can snatch them from the dogs and sheep...which is pretty often, as these are huge and proliferant trees. They've never had the runs, nor did they slow on laying, nor have any sickened and died. Had the same flock free ranging under these trees for four years now and no problems with symptoms of arsenic poisoning or death.
They say the same thing about sheep and eating green apples....pshaw! Or letting them eat tomato plants...again...pshaw! My sheep gobbled down 120 tomato plants last fall without even a burp! They are currently hoovering my orchard for any and all green apple drops.
THEY seem to have a long list of no-nos but I've never seen anyone's livestock or chickens die from eating these things.
I think, if a chicken has a set diet and you introduce apples as a treat, it could very well upset their digestion and their egg laying performance...as would anything that caused diarrhea and the resulting dehydration/electrolyte loss.
It may even by the fact that apples drop in the fall and so do the feathers....as in moulting...as in a natural decline in laying during those months.
Actually, I haven't seen anything that a chicken eats kill it....they can consume the same things pigs can and get away with it.