Nowadays the dog catcher has an employer-provided insurance plan. It doesn't provide the range of options and choice of specialists that the CEO's plan (and personal cash) does, but I don't think there's any significant difference in lifespan between people employed full time in low paying jobs vs. high paying jobs. And frankly, the difference displayed by the non-working/welfare class has more to do with failure to maintain a healthy lifestyle, than with the lesser quality of public hospitals and Medicaid-participating doctors.
100-150 years ago, medical care beyond home remedies was on a cash-for-services basis. While most doctors would accept delayed payment, barter, etc. there was also a strong cultural value to avoiding debt. People who didn't have much money didn't call for the doctor unless circumstances were really dire, by which time it was often too late. And poorer people tended to live in rural areas, where less sophisticated doctors practiced and newer medicines and medical equipment were simply unavailable.
I'd be really surprised if the quality gap between medical care of the rich vs. poor is greater today than back then. However, I think the left has done an awesome job of promoting the belief that as society as a whole has gotten wealthier, more and more people are being excluded from the benefits.
I would guess the lifespans of the dog catcher and CEO are much closer today than 100 years ago. That's excluding lifestyle choices, accident and the advent of a major illness brought on by genes, etc. However, the gap is still greater in terms of the type of health care received.