>I don't quite get the difference, patients pay a fixed amount for insurance, hospitals charge "fee for service" to the insurance. Both systems coexist, it's not one or the other.

I think their reference to "per capita" here is referring to a capitated payment structure where a provider organization is given a fixed amount per patient up front instead of billing for every service they provide. The software analog would be something like a flat subscription fee vs usage-based billing. While it's not the default in the US, it theoretically encourages providers to provide cost-effective care rather than just racking up bills on unhealthy patients.

The mechanism here is who bears the financial risk. The model you're familiar with is one where the payer (commercial insurance or medicare/medicaid) is the risk-bearing entity. They want more cost-effective care so they can protect their margins while the provider is incentivized to push a high volume of expensive care so they can boost their margins. Don't have it handy but the data on this shows providers are winning this battle with healthier, growing margins vs insurance companies whose margins generally aren't great.