If I may elaborate just a bit...
Emergency Services...Police, Fire, EMS, and Dispatch, vary greatly from state to state, county to county, and municipality to municipality. For instance, living in a Commonwealth (PA,) the lowest form of government rules. But, the Commonwealth dictates that local government (ie: the municipality) is responsible for providing, implementing, or otherwise contracting emergency services. The town I live in contracts to a neighboring town for EMS coverage. My town pays an annual fee to the EMS to cover my town. In addition, most EMS (as well as the VFD's) send out subscription cards every year. For $75, me, my family, and any guests are covered, regardless of what insurance does not, should I need assistance from the EMS. If I do not subscribe, any fees that insurance does not cover, I will be responsible for.
As a previous poster stated, the services that EMS provides can easily rise above $1,000. Every item that the EMS uses to treat the patient needs to be replaced. Sheets, pillow cases, blankets, IV needles, tubes, bandages, EKG pads, medications...it all needs replaced and this all costs money. There's also fuel and maintenance costs for the truck itself, as well as the EMT's and Paramedics wages, if it's a paid service. Hard to imagine, but there are still volunteer EMS services out there.
In addition, most Fire Departments are charging for their services as well. Around here, all the indvidual needs to do is pass the bill onto their insurance company. The FD accepts whatever the insurance pays and waives the remainder, if any.
One thing the original poster can look into is if the local EMS has a subscription fee. Sometimes if you subscribe after using the service, they may waive, or otherwise reduce the remaining portion of the bill. Sorry to hear about your sister and glad everything came out just fine. But please understand that the ambulance isn't stocked for free and doesn't get free fuel.