The following points are taken directly from an email posted on Primate-Science, an email discussion list with over 750 subscribers. Specialty training in lab animal medicine is also another option because many primates are used in research settings, so most lab animal vets have a fair amount of primate medicine training, and frequently go on to take special training in primate medicine. The nice thing about lab animal medicine is there are formal training programs at various institutions that also pay a decent salary while attending school. As for the holistic approach, I am not sure any program does that too much, simply because of the lack of time to get all the medicine aspects in.
Most veterinary colleges are state schools.
In general, they take the vast majority of students from their own states. Some schools have reserved spots for out of state students, but generally these are students from states that do not have their own veterinary schools. Students must prepare for board exams which encompass many species. There is little time other than through externships or electives to cover other material. If you haven't been interested or trained in these matters, you just won't know about primate behavior, and won't get this training in vet school.