Not true at all. In fact the poorer you are, the better health care you get - all free. It's the middle class who get crushed in America. $2000/mo insurance with $5K deductibles for a family of 4.
People are often unaware of this. I was really surprised to learn that my health insurance was completely free in WA (Apple Health/Medicaid) when I quit my job. Health insurance affordability is really U shaped as you're implying and that chasm can be hard to cross.