Good question, I'm sure there are lots of valid answers.
My perspective would be lack of exposure to the field among surgery residents, and perhaps lack of interest. The major appeal of pain to the anesthesiology resident is that it gets us out of the OR, gets us out of (real) night call, and allows us to learn and use a new skill set. Surgeons want to be in the OR, self-selected for tolerance of painful night call, and are already using a wide skill that includes the very gratifying ability to fix a patient surgically. Surgeons are also heavily invested in the skill set learned in the course of surgery residency. Learning the skill set of pain medicine takes years more. The fellowship is short, but really getting good at pain takes years more experience seeing and successfully managing the vast array of problems people can present with.
I disagree with clubdeac who said surgeons don't fix pain, that's nonsense. The medical problems that lead to surgery are often painful, and the surgery usually takes away the pain. The best part of my day is when a patient comes in for follow up telling me they are now pain free because of something I did. Surgeons already get to experience that joy in the course of practicing their primary specialty. They have no reason to go looking for it in a much tougher patient population.
Now what my colleague was probably referring to was scar-tissue related chronic pain as a consequence of surgery. More cutting does not fix the problem. One example he gave was post-herniorraphy pain. I have "fixed" this many times with injections carefully placed using ultrasound guidance with a goal of splitting adherent fascia planes. Is that not a form of a surgical procedure? Why couldn't a surgeon do this if he or she were appropriately trained?