Ah, but here again you did not prove a damned thing. Comparing expenditure vs GDP is a silly means of finding out the goals and effectiveness of social programs such as healthcare. Black Americans simply do not have any form of universal healthcare provided by the state, and if they do it is limited to children (specifically the really poor, and often times it is only subsidized and people don't pay for it anyway) or elderly, not the middle of the road poor (again, because many states have opted out of Medicaid expansion and also happen to be the states with the highest African American populations). Now, you want to compare life expectancy of these two groups without considering that life expectancy of Native Americans is pretty much on par with Indigenous Australians (but again, you want to pick a poor group to compare it to to pretend our minorities don't suffer as much as yours).
Just read this article please, Native Americans life expectancy is 2.4yrs behind American average, Indigenous Australians is ~20yrs below the Australian average life expectancy. The data is from 2009 (I think) but it still wouldn't have changed that much in the last 5 years.
http://www.un.org/esa/socdev/unpfii/.../SOWIP_web.pdf