Extremely poor people may not pay for care, but be assured that in America, they get no where near the same level of care.
And if you're poor and have cancer? Most other western countries will give you a chance.
There is a much deeper problem relating directly to this topic. Transportation. Access to real transpiration is THE BIGGEST FACTOR in escaping poverty.
Uber isn't public transportation. A train is about $2 ~ $3 in most cities. In an Uber that would be a $10 ~ $20 ride. Multiply that by 7 days a week to and from work, and there simply is no comparison. Many cities have discounted fare cards for the poor as well. The structure of American cities hurts the poor.