Yes, it matters a lot how you die. For instance, there are 2,900 hippopotamus-related fatalities worldwide every year. Zero of those occur in the US. If you compare the US to Subsaharan Africa by hippo fatality, all you learn is that Subsaharan Africa has hippos.
But they have less cars, to take an example. Dead is dead was my point and in whatever country you live, you will deal with the cars, lions, tundra or whatever.
Sure, and it does seem to be true: life expectancy in part tells you "this country has more cars than hippos". The car/hippo ratio is a very different concept than "quality and outcome of health care systems".