The third-party payer system hurts people who pay premiums into the system. It may give them a higher quantity of services, but it still hurts them.
This system hurts them by giving them more services than they would consume if they knew how much they were paying. By hiding the true costs of medical services, the system induces consumers to consume more of those services. Someone has to pay for those services consumed. It is the consumers who pay for those services through their premiums (or through taxes in the case of government-run systems). If the system were more transparent, consumers would get fewer services, but they would also pay less money for them.
Thus, consumers are hurt by paying more than they otherwise would for services that they would not consume if they were aware of the costs.