Gavin Neil is not setting up a false dichotomy. His comment is that it is not "of course" that competition in health care promotes efficiency and quite rightly uses the U.S. system as an example. He is not commenting on the lack of coverage and under-coverage.

One can also look at the Netherlands and their reforms to establish competitive private health insurance coverage for all and the assumed "of course" would stimulate more efficient health care delivery. Costs skyrocketed and pushed up Netherlands to among the highest of GDP spending on health. 

The notion of "of course" has been questioned by the most mainstream of economists since Kenneth Arrow wrote his seminal article, "Uncertainty and the Welfare Economics of Medical Care", in 1963. Countless research and published articles over the decades say 'not of course'.