You more know details than I do about primary killers of those in the paleo environment. I always understood it more generally, that the infant/youth mortality rate was high, but then leveled off to rates more comparable to modern man beyond the age of about 10yo. But what you say makes sense; someone with a higher inflammatory response might fare better in that environment.
Is this really a flip side? In one case, we're talking about antibiotics that are taken for a short period of time when a person has an infection, and in the other case, we are talking about a chronic condition, where the immune is activated do to daily dietary intake.
First a point of clarification: are you talking about neolitic or paleolithic here? Neolithic man started eating grain and it is correlated with a sharp reduction in lifespan and a reduction in size/growth/development of people compared to their paleolithic ancestors. There are other factors here besides diet. For example, fighting for land became more prevalent in the Neolithic age and a lot of people probably died young in wars. Still, the fossil evidence of stunted growth seems pretty compelling.
Could shifting to a more inflammatory grain-based diet help someone fight disease? I'm no expert, but I am not sure it would. I seem to remember reading that extended, chronic, inflammatory response actually weakened the immune system over time because it basically added stress to the system, depleting its resources. Could such a diet help in an acute way? e.g., stimulating a response when needed? That's an interesting question.
Coming back to the original point, I do think the basic inflammation premise of a Paleo diet is sound, because I believe there is compelling evidence that the modern American diet is making people sick, and that one big reason for that is the predominance of grain-based food sources throughout our food chain. And I'm ignoring the elephant in the room here and not even talking about refined sugar/corn syrup. Inflammation is only one aspect of Paleo. Preventing insulin hyperactivity is also a key aspect of the diet. In fact, its one key reason paleo typically allows fruit and vegetables without concerning itself too much about carbs (other than cutting out starchy tubers), because the fiber in those foods helps slow digestion, increase satiety, and dull the insulin response.
Anyways, to me, understanding all of this makes it clearer why someone might do paleo, then modify it to purposefully spike insulin before a workout, or add milk to achieve IGF-1 benefits (which to my knowledge are suspected but not proven; of course, what IS proven in nutritional science, heh...). The basics remain the same, and I believe they are pretty sound.