Maybe accupuncture, in this case, operates in the same area as horse whispering, exercising trust by engaging awareness and attenuating hostility. Operant conditioning has lots of animal applications.
They can’t subject them to tranquilizers for weeks, and the pain leaves the injured animals restless, so they have to be dealt with, while fully lucid and agitated by their injuries. Familiarizing wild animals with being handled, even while in pain, and for the purpose of carrying out possibly painful procedures, has a unique set of problems to solve.