I just thought of something that puts this in a little clearer perspective.

The main reason for calling an ambulance is not to get transportation to a hospital. The main reason is supposed to be to get the emergency care of EMT's and/or paramedics. So just saying that you were in too much pain to drive is not a compelling reason, on its own, to need an ambulance. That's just a compelling reason to call a taxi. That's the argument the insurance company would make, and they would have a good point.

If you have any prior history of having been diagnosed with ovarian cysts, the insurance company would further argue that you could have known that the cysts may have been the cause of the pain and that these cysts acting up is not really a severe enough emergency needing hospital-based care.

If you did not have a prior history of this diagnosis, and even if you did, I would take it that they must have done a scan in the E.R. to be able to tell you that this was the problem. Those scans can cost thousands of dollars. That's what I would think is the main item making your cost be as high as it is.

Now that I think about it, you would be entitled to have that scan paid for by your insurance company in any case. Even if you had driven yourself to an urgent care center, the doctor there would probably have sent you for a scan. That's pretty much what it takes to identify the source of severe abdominal pain. So check exactly what is the breakdown in the costs you incurred on that day, and see what the insurance did and didn't pay for. I can't see how they can get away with not, at least, paying for the scan.