He makes a compelling argument, but like Haider says, ...it's an all too simplistic one.
Take the altruistic humanitarian aspects out of it and simply look at the pragmatic and selfish look at it.
As a Canadian, the concept of people living in a prosperous civilized society and not having healthcare is anethema to me, but aside from that... forget altruism, and look at practicality.
Many of the same people screaming about universal healthcare and the prospect of sharing the costs, have never had a fire in their home, but they are paying for fire departments to put out fires in the homes of their neighbours. Why is that? ...so that when their neighbours house catches fire, ...it doesn't spread to their own.
Universal Healthcare is really no different. I don't want to be catching deadly tuberculosis or other preventable and treatable deadly communicable diseases, because someone didn't have access to healthcare.
The people who scream about not wanting to pay for someone elses healthcare don't seem to fathom that that is EXACTLY what they are doing right now, ...except they are paying through the nose.
It's the same with the police. People share the cost for law enforcement. They pay for police to lock up criminals and put away bad guys. Whether they've needed the police themselves is irrelevant. you pay to have the bad guys locked up, so they'll be off the streets and not breaking into your homes. If one does, the police are there for when you need them. Until you do... they are there for your neighbours. It's no different.
As a concept, I am firmly on the side of universal healthcare. How your country goes about implementing it... well that's another story. Your system as it stands is unsustainable and is a train wreck waiting to happen.