The ticks aren't really the problem, it's the parasites inside of them that are bad. Those parasites go right through the chickens and geese ("like shit trough a goose"), and end up in the droppings.
From what I've read it's the baby ticks that like to hitch a ride on geese, once they mature a bit they drop off and look for a larger mammal.
I've also read that chicken get salmonella from eating diseased flies. Like you say, the salmonella runs right through the chicken, doesn't really effect them, but it gets passed on through the eggs and poop.