I had a minor procedure a few months ago. Hospital, surgeon, etc, are all 'in-network' the anesthesiologist, however, is not. And there is only one 'group' for anesthesiologists in our town.
Another major annoyance -- if you have surgery, the hospital usually gets their money from you right away. However, you're going to spend the next 18 months receiving random bills from various different firms representing nurses, doctors, lab technicians, etc. related to your procedure, many of which come down to "stuff we decided to do while you were unconscious."