Some patients said they were puzzled why relatively short rides could cost so much and added that the bills only contributed to more stress during their recovery period, when their injuries prevented them from returning to work. Others questioned whether a regular ambulance, a much cheaper option, would have been a more appropriate response for the injuries they sustained. Some patients even contended that they could have reached the hospital more quickly by road than air.

One of these patients was Diana L. Kidd, a family lawyer in New Paltz, N.Y. After a motorcycle accident in July 2012, she was taken to the Catskill Regional Medical Center. From there, an Air Methods helicopter transported her to a trauma unit at Westchester Medical Center. The company charged Ms. Kidd $36,646, a bill that fell to her because her insurance did not cover ambulance transportation.

She has not paid the bill and is countersuing Air Methods, which had sued to collect the payment. Ms. Kidd has calculated that a regular ambulance would have made it to the trauma center in well under the one hour and 55 minutes that she said she was charged for. “I could have been taken by ambulance,” she said. “There is nothing in the record to indicate that I couldn’t have been.”

Air ambulance companies rarely collect the full amounts when they go after patients, and they often say they will lower the bill in the hope of getting something. Ms. Kidd said Air Methods representatives had offered to cut her bill to $10,000 if she provided personal information to show that she lacked the money to pay, something she declined to do. Mr. Kendall, the rancher, said Air Methods had offered to lower his bill to $33,000, a sum he said he thought was still too high. Mr. Kendall said that he told the company he would not pay more than $10,000.

While Air Methods may be willing to reduce bills, it also pushes hard in court to be paid. The company, for instance, put a lien on the house belonging to Mr. Dotson and his wife, Patricia, as it pursued its claim. Most of that amount was for transporting Ms. Dotson to a hospital after she fell from a horse. By filing for bankruptcy, the Dotsons were able to expunge the Air Methods debt, but Mr. Dotson said that action had damaged their credit.