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.

Is there a debate informed by decent evidence, though? As far as I know, no high-quality study has ever shown acupuncture to significantly outperform sham acupuncture, let alone outperform usual care. In my experience, studies cited by lay acupuncture advocates are usually either preliminary types of studies (uncontrolled or unsuitable control intervention, non-randomized, small N) or actually involve doing something other than acupuncture, such as running an electrical current through the needles.