Why would anyone consider comparing diets of different species more relevant than comparing diets within different populations of a species (ie, "civilized" humans to modern hunter-gatherers)?
To make an analogous comparison of a generally omnivorous family, look at the bears (different species within a taxonomic family, similar to humans and chimpanzees). The diets of bears range from purely herbivorous (pandas), to largely herbivorous (inland grizzlies, black bears) to purely carnivorous (polar bears). Does the diet of any one of these species imply that the diet is optimal for another?
Species are adapted to their environment and its food resources. To conclude that humans (successfully adapted to virtually every ecosystem on earth) should model our diets on apes (a group of animals inhabiting exclusively tropical forest habitats) defies logic and evolutionary adaptation.
Your referenced author (Milton) acknowledges the role of animal food sources in human evolution here: