Not sure who the doctor is, but pins typically don't break that easily. I don't know about arms but with legs, if one of the pins were to break, you can still turn and finish lengthening. Normally, external fixators on Tibias have at least a dozen pins (or more), so if one pin breaks the rest can still support the weight and the keep the bone is place until the lengthening is finished. It's not unsual for doctors to remove a pin or two if there is an infection at the pin sites.
If the broken pin is inside, and the pin site is still open, it most likely needs to come out to avoid potential infections.