http://www.newsweek.com/us-leads-industrialized-world-premat...
This is unlikely to affect the stats. Giving poor people access to health care does not improve physical health in any measurable way. It does make them feel better, however.
Of the various public health concerns, infant mortality is one of those that are most directly addressable with medical care directed at the poor. Improved access to health services won't get a poor person to change his diet, but can be very effective in catching potential complications from pregnancy, treating infections in neonates, etc.
Also, the study you linked-to doesn't support the claim you're making ("Giving poor people access to health care does not improve physical health in any measurable way."). The study looked at just three physical health outcomes, after two years: blood pressure, cholesterol, and glycated hemoglobin (a measure related to blood sugar level control). These are lifestyle-related measures unlikely to be affected in merely two years.
Moreover, the study is inappropriately designed to test the conclusion you assert. First, it is based on giving a random sampling of people access to Medicaid ("In 2008, the state of Oregon drew names by lottery for its Medicaid program for low-income, uninsured adults."). But to address lifestyle diseases, you need to build a culture of intervention over a long period of time. You can't do this in just a few years targeting a few members of the community. Second, the study doesn't measure the impact of "access to health care" but rather access to Medicaid. The non-control group still received healthcare services, they just did so through the emergency room and by doctors' visits that went unpaid ("Medicaid decreased the probability of having an unpaid medical bill sent to a collection agency by 25 percent.").
Increased access to prenatal care has a very clear correlation with reducing early births (and that Oregon study focused narrowly on improvements in blood pressure, cholesterol or glycated hemoglobin. Reducing infant mortality isn't in there.).
Edit: Also, how much impact do you think earlier diabetes intervention will have in a 2 year period? I can at least conceive of earlier intervention having some impact after 5 or 10 years.
The graphs in the article showslife expectancy at birth, which is a number dominated by infant mortality rate. For life expectancy at age 65, the US is slightly above the OECD average. Comparable to Germany or Norway. See Page 19 of this PDF: http://www.oecd-ilibrary.org/docserver/download/8109111ec004....
The other OECD countries started pulling away on infant mortality starting in the 1970's: http://www.conferenceboard.ca/Files/hcp/health/health2012_in....