In the same sense that it would protect unconscious people from incurring enforceable debts?
A sane system would look at the incentives structure to devise cartel rules to encourage the individual behaviors that lead to the best group outcome.
The injured party desires swift and effective treatment for their injury. They also desire such treatment to be affordable, preferably at no additional out-of-pocket cost.
Onlookers may wish to help in the moment, but they do not want to incur any future obligations by doing so.
Medical providers want the customer brought to their facility, first to assist with the injury, and then also to be rewarded for producing better outcomes due to their care and expertise.
The move that makes sense is for injured parties and onlookers (they cannot know in advance who would be the unlucky one to get injured) to cartelize, and each pay an amount in advance so that the statistically predictable annual number of ambulance rides are all (theoretically) already paid for. And since it could damage the patient to delay care by attempting to verify cartel participation, it really has to include everyone, or ignore free riders. So the cartel becomes a branch of government, and it pays for ambulance rides with some form of tax. Then to prevent gaming the system by private ambulance companies, the cartel can either announce limits on what it will pay for during one ambulance ride, or it can run its own ambulance service.
And to further control costs, if they haven't already determined that it is an emergency with major traumatic injuries, the dispatcher can even just ask the caller if an ambulance is not needed. Most people can at least recognize if someone else does not need an ambulance, and maybe just needs an ordinary ride to the hospital without all the equipment and paramedics. The dispatcher can summon a cab, or Lyft, or Uber, or a bicycle rickshaw, or church bus, or shuttle van, or any other type of local transportation service, and pay their prevailing rate for a prompt, on-demand ride to some form of medical care facility. Since the patient would have to be conscious in order to get a not-ambulance ride, they could either wave it off, or tell the driver to go to their pick of clinic or hospital and have the ride paid for by their ambulance tax.
Other moves create perverse incentives to ignore injuries or hinder the care of an injured person.
Similar analysis indicates that hospital treatment for life-threatening injuries and other health emergencies should also be paid for out of taxes. The rest of the medical system could possibly operate under a different model, but I think most people would rather not be forced to choose between death and bankruptcy--for themselves or anyone else--when there's a dearth of time to think about it.