I Don't Understand How "Insurance Adjustments" Work

I have a high-deductible PPO medical plan: if I go to a Doctor, I pay the bill directly. It's not unusual for there to be a discount "If you pay at the time of services." Generally, it's around 25%, but sometimes it goes as high as 50%. I interpret this to mean that the work and "insurance adjustment" associated with processing an insurance claim works out about the same. And it makes sense to me that insurance companies pay a little less than the Doctor's "walk in" charge in exchange for access to patients and the assurance that, even if the amount is lower, the HMO is going to cut the check at the end of the month.

Tina, on the other hand, is in an HMO. We just received one of those "This is not a bill" statements of insurance behavior. Tina's surgery was billed by the doctor as X. The insurance adjustment was -78%! I'm baffled. The premium (as it were) being paid by the surgeon to participate in the HMO is incredibly out of whack with the "walk in" rate. I feel that there must be an economic reason for the surgeon to keep their nominal rate out of whack with their expectation.

Now, it may be that the Doctor knows that they can charge X to a walk-in and that the more specialized the Doctor, the greater the disparity between X and the insurance payment. But just from a bookkeeping standpoint, I would think the Doctor would attempt to bill the insurance company something in the realm of what is expected (more than what is expected, to pressure the company to raise its payments, sure -- but not 4x the expected payment!).

I wonder if they can write off on their taxes the insurance adjustment.