Dr. Roylott's baboon was probably not a native of India only because very few baboons are native to India. Baboons are from Africa and parts of the Arabian penninsula only.
The original source of information stating that the baboon, and the cheetah, for that matter, were Indian animals was Helen Stoner. We can have no doubt that even if Dr. Grimesby Roylott did import his baboon through a correspondent in India, he knew full well that the animal originated elsewhere. It is important to note that Holmes never entertained this fallacy- he never stated that the baboon was an Indian animal.
Wherever Roylott got it, the baboon was probably of the species Papio ursinus, the largest of the baboons and approximately the size of a large dog. It is greyish brown with a green tint along its back. Or, the opposite can be true, and the smallest species still commonly referred to as a baboon, which IS found in India, could be Dr. Roylott's. All baboons are well adapted to life on the ground and actually are usually found in groups in the wild. Watson's likening of the baboon to a "hideous and distorted child" seems a little harsh, but he can probably be forgiven given the dark and surprise accompanying the event.