He refers to a story about a man who failed to pay an annual fee for fire protection and then, when his house caught on fire and he called the fire department, the fire department refused to show up.
They wouldn't even let him pay up ex post. David notes that this is a government-run fire department and thus the story is not much of a moral reductio on the market. Arguably a private company would behave the same way, sometimes, but it 's odd to claim that government failure reminds you market failure is possible and so let's damn the market. By the way, markets do pretty well at setting up schemes with a penalty for late payment; that's how my mortgage works.
I would make a broader point. Any social system must, at some stage of interactions, impose some morally unacceptable penalties. If you are very hungry, and you shoplift food, they still might prosecute you. If you don't pay your taxes, and resist wage garnishes, they might put you in jail. If you resist arrest, they might, at some point in the chain of events, shoot you while trying to escape. Somewhere along the line there is a doctor who can treat your rare disease except he doesn't feel like working so much, and so he lets you die or suffer; you can find both private and public sector examples here.
Social systems proceed by (usually) covering up the brutalities upon which they are based. The doctor doesn't let you get to his door and then turn you away, rather his home address is hard to find. The government handcuffs you so they don't have to shoot you trying to escape. And so on.
To borrow language from Thomas Schelling, social systems involve costs in terms of both "known" and "statistical" lives. It's the sum total of costs which is important. It's fine (though controversial) to argue that a "known" life should be more important than a "statistical" life, but it's not dispositive to pull out one example of a "known" life and draw a significant conclusion from that anecdote. That's what we teach students not to do in first year principles, sometimes citing Bastiat, the seen and the unseen, and so on.
I don't favor the policies of this fire department, but simply pointing out the vividness one of these social brutalities doesn't much influence me about the broader principles at stake.