In a very basic sense, psychologists do study behavior and the origins of that behavior - much of which stems from our cousins in the animal kingdom. You are correct that much of our behavior is strikingly similar to apes, chimps, etc. The fact that we share so much DNA in common is one of the reasons that chimpanzees are often used by scientists to study new drugs, theories of complex cultural reactions, etc.
However, I would be remiss if I didn't mention the one thing (aside from the .1% of DNA) that separates us. And that is, the development of a complex verbal language. While there is no doubt that apes/chimps communicate with their own language and that they are capable of using limited simple sign language to communicate with us, humans are still the only creature on the face of the earth that have developed a complex verbal communication system. Dr. Steven Pinker has written some amazing literature regarding this.
So, while I would agree with you on many of your previous thoughts, I think that psychologists are different from "primate-ologists" in that we rely heavily on verbal communication from our clients. In general, our study of the human condition is not only informed by our ancestor's behavior, but by our contemporary's words. :)