Health insurace CAN and WILL pay for auto-accident related bills, if there is no coverage available under an auto insurance policy for the claim. Did your health insurance pay for the rest of the bills related to the accident? If so, then they wouldn't have denied JUST this one for being related to an auto accident. So there are some other questions you need to ask.
Was the bill ever submitted to your health insurance? If not, why not? If so, did they deny? Why did they deny? If they denied it for being not medically necessary, then you ARE going to be responsible for paying, unless you want to try appealing it with your insurance company, but I don't know how far you'd get. If you don't need special care or equipment during transport, then an ambulance wouldn't be medically necessary.