Inequality, health and the Spirit Level

I am at Sussex university discussing a paper by Richard Wilkinson, author of the Spirit Level.  His main point is that many outcomes, notably health are not correlated with GDP per head, but with inequality.  So for example,

 

is the relation between life expectancy and GDP per head i.e. declining.  But

is the relation between inequality and life expectancy. 

So Paul Stoneman asks a nice point.  He can see that making a poor person richer might riase their life expectancy.   But the logic that inequality matters says this:  making a rich person poorer, raises the life expectancy of the poor person.  This seems to me a substantial objection to the theory that inequality determines life expectancy and health.