Medicare was introduced 1965 in the US. Public health coverage for the elderly existed by 1950 in Sweden, but full universal coverage dates to 1955 in Sweden (a public health insurance was founded in 1891, and public municipal public health existed for even longer).
In 1950, before Medicare, and before Universal coverage in Sweden the difference was +2.6 at birth and +0.3 at 65. In 2001-2005 the difference between the Sweden and US was +2.7 at birth and +0.3 years at 65. Identical!
First, regarding the life expectancy at birth we can note that 50 years of different health policy, labor mark policy, welfare state coverage seems to have had zero effect on total outcome.
Last note: around 1900, before the expansion of the welfare state, the estimated life expectancy at birth was 54.0 years in Sweden and 47.3 years in the US, a difference of 5.3 years, twice the current gap.
If you scroll through Tino's blog, you will find various critiques of The Spirit Level. On the health care point, I would stress that Hansonian results also can be used to argue for the extreme exercise of monopsony power, so don't think the policy implications of this are so simple.