Weird accounting

I manage my mother's affairs. She's been in a nursing home since she was hospitalized last July for 11 days. So all of a sudden, on December 26, I get a bill from the hospital. I didn't expect one since she has a Medicare Advantage plan, but apparently there is a copay for this. Here's the itemization of the bill:

CT Scan: $5,075
EKG/ECG: $198
Emergency Room: $2,609
Laboratory: $3,429
Medical/Surgical Supplies/Devices: $2,192.76
Occupational Therapy: $2,901
Other Care Items: $3,734
Pharmacy: $1,369
Physical Therapy: $5,913
Room and Board: $46,838

Total: $74,259

In case you're wondering, room and board comes to $4,258 a day. That's a pretty fancy hotel.

The good news is that the insurance company paid $6,605.43. Don't know how they got to the 43 cents. Then there was an "insurance adjustment" for $67,454.12. The net result is that my mother owes 200 bucks, which she does happen to have so I sent them a check as I assume this is legit, but how am I to know?

So what's going on here? The answer is that they have a negotiated price for all this stuff with the insurance company, which is less than $4,258 a day for room and board, and comparably less for all that other stuff. The list price is entirely fictitious, except that they will in fact try to extract it from uninsured people. Why do they do this? Beats the hell out of me. It seems completely nonsensical. And I'm a health services researcher.