Thanks for your answer Alexandria,
As you didn't seem entirely confident about the innervation in the skull bone, I ended up asking the neurosurgeon, and she indeed only anaesthetises the skin surrounding the drill hole and the subcutaneous tissue as the bone does not have nociceptive innervation in that area. So you are right for the leg: if chopped off, you would still feel the pain from the nerves in the bone. In the case of deep brain stimulation however, the skull does not have nociceptive innervation in the area where the holes are drilled.
This leaves the question of why there are some exceptions to bone innervation, but that's a problem for another day.