I wonder if there is a fundamental difference between voluntary fasting (like humans do) and enforced starving (on the mice). Withdraw the food and the mice can not know if they will have something to eat in the future. And that arguably will induce enormous stress on the animals. Not so on humans. We know exactly we can have food whenever we want, and that little hunger will quickly pass, no stress induced.
Will that affect the immune response? I suspect yes.