Phylogenetically, and in terms of their ecological niche and morphology, apes are less similar to small monkeys than to paleolithic humans. Therefore, absent evidence to the contrary, we should expect that we can predict ape behavior better by looking at paleolithic human behavior than by looking at monkey behavior. This is a testable claim. Naive subjects can try to predict ape behavior by using different pools of evidence, information about either monkeys or paleolithic humans. The amount that one can know about a by observing b is correlated to the amount one can know about b by observing a. This consideration really should narrow the range of hypotheses we consider when speculating upon our innate behavior. If all other apes and monkeys possess a feature, including 'innate behavior' in so far as 'innate behavior' is a valid conceptual construct, we probably also possess that feature.
It may not be much, as a theory of psychology, but it's a start.
While making some correct predictions, this model certainly has its failures. Some of these failures seem relatively unthreatening. For instance, because we eat far less fruit than most monkeys or apes do, we tend to have much lower concentrations of vitamin C in our blood than do other primates. We can explain this difference easily because we can conceive of a clear difference between the concepts 'innate biochemistry' and 'biochemistry'. Other theoretical failures are more perplexing. One might speculate that paleolithic humans lack thick body hair because they use fire. Some day, differences between preserved Habilus and Erectus tissues might even partially confirm this, but one then has to ask why they and Sapiens but no other apes can use fire. Habitat is surely somewhat relevant, as most apes live in very heavily wooded locations, which present difficulties in the use of fire. Other apes also possess generally inferior tool-using abilities when compared to Habilus, Erectus or Sapiens. Most distressing, paleolithic humans tend to produce a much larger range of vocalizations than do other primates, a behavior that seems more typically birdlike.