The Church on Health Care: "Defend the Private Sector!" (?)

I'm quite sure that I do not know how to solve the problems we have in this country regarding access to health care; I'm also pretty sure that the bishops don't know how to solve the problems either.  (Nor do I expect them to know.)  I find the statements of individual bishops on the topic to be interesting, primarily because their views often appear to be shaped by their own cultural or political views as much as by Church teaching.  Take, for example, the statement of the Sioux City bishop, R. Walker Nickless:

[T]he Catholic Church does not teach that government should directly provide health care.  Unlike a prudential concern like national defense, for which government monopolization is objectively good – it both limits violence overall and prevents the obvious abuses to which private armies are susceptible – health care should not be subject to federal monopolization.  Preserving patient choice (through a flourishing private sector) is the only way to prevent a health care monopoly from denying care arbitrarily, as we learned from HMOs in the recent past.  While a government monopoly would not be motivated by profit, it would be motivated by such bureaucratic standards as quotas and defined “best procedures,” which are equally beyond the influence of most citizens.  The proper role of the government is to regulate the private sector, in order to foster healthy competition and to curtail abuses.  Therefore any legislation that undermines the viability of the private sector is suspect.

Does the Church actually teach that "a flourishing private sector" is the predominant concern when it comes to a society's provision of health care?