I understand what you're saying but it sounds like you know what it means to separately ask about animal intelligence in the sense relevant for evaluating, say, crows vs pidgeons, and that question obviously is not just about animals having sophisticated immune responses.

I would venture a guess that nearly all animals will turn out "intelligent" if all we really mean is they things like complex immune responses to disease, or complex coordination needed to grow an embryo. Those matter and raise profound questions about how incredible natural selection can be, but I would wait for an actual sin of commission before treating any commentary on animal intelligence like it neglects to appreciate sophisticated behavior of cells.