Yes, that's often the case. If you're really poor, you qualify for governmental support in some form, and you're not vulnerable to financial loss because you have essentially nothing to lose anyway.
A lower middle-class person who gets sick with no health-insurance, risks losing the small amount of wealth he has, and to have the income of the family drop to welfare levels. A person with essentially zero wealth, and income which is already at welfare-levels is immune to financial woes of this sort.
According to CNN, medical debt is involved in 60% of the personal bankruptices that occur. I'm guessing that's mainly people who are neither wealthy nor dirt-poor.