Baboons, social intelligence, and large brain size

Since I have some background in human evolutionary ecology, I am interested in why humans have such big brains. There are several hypotheses out there for what ecological factors drive large brain size, some of which I've discussed on this blog.
In an article by Nick Wade in the NYT about the social smarts of baboons, he and Dr. Seyfarth give their opinion:

It is far from clear why humans acquired a strong theory of mind faculty and baboons did not. Another difference between the two species is brain size. Some biologists have suggested that the demands of social living were the evolutionary pressure that enhanced the size of the brain. But the largest brains occur in chimpanzees and humans, who live in smaller groups than baboons.

But both chimps and humans use tools. Possibly social life drove the evolution of the primate brain to a certain point, and the stimulus of tool use then took over. Use of tools would have spurred communication, as the owner of a tool explained to others how to use it. But that requires a theory of mind, and Dr. Cheney and Dr. Seyfarth are skeptical of claims that chimpanzees have a theory of mind, in part because the experiments supporting that position have been conducted on captive chimps. “It’s bewildering to us that none of the people who study ape cognition have been motivated to study wild chimpanzees,” Dr. Cheney said.

“Baboons provide you with an example of what sort of social and cognitive complexity is possible in the absence of language and a theory of mind,” she said. “The selective forces that gave rise to our large brains and our full-blown theory of mind remain mysterious, at least to us.”