I certainly don't know how much of our immune responses are collective and how much is from some actual neural processing. I think our understanding is at a stage where discussion and even vigorous arguments is healthy. It's unhealthy to simply accept one theory without question.
One problem about the brain/immune response is that many of the pieces have multiple roles in the body. For example, cortisol inhibits parts of the immune system, but it is also used for several other functions. If you're being chased by wolves, your brain will boost cortisol to boost your chances of survival. However, it's also telling your immune system to shut down (to save resources for running?). If the wolves hadn't been there, your brain might have sensed a viral infection and reduced cortisol production. So, there isn't really a 'general' in charge of the immune system command network; cortisol is controlled by a gland with multiple inputs. Mutations where these conflicting demands reduced survival died out, so we've got these fairly simple independent systems with possibly inconvenient interconnections working collectively in ways that overall increases our survival.
So, if I'm imagining my body fighting a viral infection, I don't see a genius commander deciding troop deployments and movements of supplies and so forth, with all messages coming from HQ. I see a bunch of cells with simple responses acting collectively in ways that evolution has weeded down to something that works, with various glitches and unfortunate miscommunications, friendly fire and careless destruction of the landscape.