What about "The Good Samaritan"?
It would be an even better if "the church" took it upon itself to provide medical care for free (funded out of generous donations). Some churches do provide some aid and assistance to those unable to provide for themselves.
The difference between a church providing free medical care and the government is that one voluntarily receives the funds to provide aid while the other takes it under rule of law (and arbitrarily determines how much to take). God asks for 10% but imposes no controls to insure that the church receives it. The modern government wants far more than that. God also doesn't make a distinction between what percent the "rich" and the "middle class" should give to the church.
Like I said, I was glad that the RCC provided these services where they did not exist. It might even be arguable that Catholic Charities, or some such organizations that exist simply to give things to people should be protected by the same rules that govern essential church functions. These functions are already protected by exemptions in the law that prevent a woman from suing the RCC under equal rights laws to ordain her as a priest.
But Catholic universities, hospitals, and perhaps other entities are competing in the free market, and sell their services alongside other providers, both private and governmental. Sometimes a government mandate is financially onerous on private entities, if you give an exemption for it to government and nonprofit entities, you've created an unfairness.
In a way, this is the Catholic Church's "social justice" power coming around to bite it on the butt. Sort of a payback for all the years the RCC has been championing the minimum wage, for instance.