[gizmo686]

All good points, but you also should consider the plausibility of it being a correlation. By this I mean that there seem to be clear candidates for a common cause between no insurance and high mortality, for example: income.

Once you control for this, and other potential common causes, your case for causality becomes much stronger (or non-existent).

[Fomite]

If you had read the paper linked above, you'd note they controlled for income.