Maybe playing devil's advocate here, but if it was the ambulance's fault then the ambulance company's insurance should be paying for all of the medical bills, including the ambulance ride. And the bill for the ambulance ride pays the EMS workers salaries and the vehicle maintenance.
The amount of profiteering in the medical industry is obscene, but I'm not sure this is an example of it...
I'm not a lawyer, but it strikes me that this could be exactly what is happening. The ambulance company's insurance wouldn't pay the hospital directly, they aren't health insurance. So instead, the cyclist's health insurance footed the initial bill. Then they went after the cyclist for his deductible/copay/whatnot. Now he has to get the money from the ambulance company. If this was vehicle on vehicle violence, he would have gone to his auto insurance, who would have in turn went after the ambulance company's insurance, but he might not have auto insurance or auto insurance might not be willing to get involved because he wasn't driving. So he has to go direct to the company. Wouldn't be shocking if the company pushed off any non-legal petitions from him because he doesn't have the name weight of an insurance company with lawyers on retainer, so now he is seeking a legal remedy. Insurance doesn't just work always, there is often a degree of negotiating and litigation involved in these exchanges, especially if one party disagrees with another on matters of liability