After his son was hit by a car in San Francisco and taken away by ambulance, Karl Sporer was surprised to get a bill for $800.

Mr. Sporer had health insurance, which paid for part of the ride. But the ambulance provider felt that amount wasn’t enough, and billed the Sporer family for the balance.

“I paid it quickly,” Mr. Sporer said. “They go to collections if you don’t.”

That was 15 years ago, but ambulance companies around the nation are still sending such surprise bills to customers, as Mr. Sporer knows well. These days, he oversees the emergency medical services in neighboring Alameda County. The contract his county negotiated allows a private ambulance company to send similar bills to insured patients.

In most parts of medical care, you can choose a doctor or hospital that takes your insurance. But there are some types of care where politicians have begun tackling the “surprise” bills that occur when, say, patients go to an emergency room covered by their insurance and are treated by a physician who is not.