Double billing

I was curious about how anethesiologist and CRNA's bill their services. I understand the meanings of the modifiers QK, QX. But both charging the same amount seems unrealistic to me.
Say for instants: Anethe. introduces him/herself to pt, no assessment, leaves and then when ready for OR, the CRNA comes in and does assessment, goes with pt to OR, administers sedation. After that, patient doesn't remember anything.
If the CRNA gives anesthetic agents, while Anesthe. MD is in the room then leaves and CRNA completes the rest of the "procedure", how is this billed.

Also, why is the patient not given the option of chosing to have just MD?
Pt gets billed same amount for both MD and CRNA, insurance pays half, so the pt is responsible for other half. Is this not "double dipping" in a sense.

Case is one I am reviewing right now, need some input.

Thanks
Cindy