Note that although the DNA is the genetic material, a selective pressure such as the threat of predation acts on organisms. Very rarely would selection act directly on the DNA. Rather, the correlation between carrying a snippet of DNA and not getting eaten causes that snippet to become overrepresented in the population over time.
I may misremember some of the details, but that's the gist. Your body basically generates antibodies via an evolutionary algorithm. Wikipedia has a good explanation. Keep an eye out for the word "selection": http://en.wikipedia.org/wiki/Somatic_hypermutation
Hey, look at that. Wikipedia also has this enlightening article: http://en.wikipedia.org/wiki/Unit_of_selection
This suggests that it takes a complex organism to fight disease. Once multicell organisms developed do you think an immune system was the first type of organized intelligence or that foreign invaders and parasites served as a catalyst to ever more complex systems?
As for the brain having some sort of monopoly on "organizing intelligent bahavior", that is a complex issue. I wouldn't say that the adaptive immune system necessarily possesses intelligence. It consists of many small and relatively simple components that interact to produce complex behavior. Realize that during somatic hypermutation, the immune system is not intelligently choosing which mutations to generate. It simply generates a random sample of all possible mutations and then sets up a simple selection process that produces a result that looks intelligent to us.
On the other hand, one could plausibly make a similar argument about the brain's intelligence being the product of the interaction of individual neurons. Many people believe that our brains are no less deterministic than a silicon-based computer. Complexity is complex.
Anyway, to give you another example, cancer cells are subject to greatly increased mutation rates, and mutations that result in faster growth or better recruitment of nutrient-supplying blood vessels (vascularization) will quickly become fixed in the tumor as the cells with that mutation overtake the growth of others. This also provides an example where selection at the cellular level is at conflict with selection at the organismal level. Within the tumor, selection favors faster-growing cancer cells, but these same cells are clearly the most detrimental to the organism as a whole.