No, it's because ambulance service in Denmark is a public contract. Private citizen don't pay out of pocket.

Essentially, the state (or region) contracts a company to deliver ambulance services. The contracts usually last a few years and are limited to a region.

Furthermore, the company that wins the contract (usually lowest bidder) is held accountable is too many responses are too slow, etc.. usually with hefty fines.

I guess you can call it privatization, but it's more of a regulated monopoly. Ultimately, these things outsources uncertainty from the state to the private sector. I'm not convinced it's always a good idea, since companies can just factor the cost of fines into the contract... Granted if there is competition, it can drive the prices down a LOT.

British Columbia, Canada, does this as well. Ambulatory services are provided by contractors. So are most paramedical services.

And public contract it is in many other places, like where I live (Finland). Local government pays ambulances, I pay a sum to the local government out of my pocket after I have used ambulance.