Counterpoint: if not all doctors are equal, and better doctors charge more, having more money makes you able to afford better doctors. If your doctor is 10% better at detecting cancer for example, that may translate to a longer life.
My intuition tells me that at a personal level (instead of statistical on a population) it's even more important to avoid things that can cause an early death, because at the statistical level it's "compensated" by people to which it will never happen, but not at the individual.
Nutrition and fitness are very important to delay aging, which will kill you in the end, and improve your chances at surviving "death chance event" like getting a cancer. But having top professionals help you face these events (cancer, depression, car accidents (by means of having a better car, the help is indirect but still comes from money)) can have a huge and maybe even bigger impact.
As for the stress and social connections, I'm not sure I agree. At an equal amount of stress/social connections, someone with high wealth will have most/all of the time more options compared to someone with low stress. Sure some people might be putting pressure on themselves, but there is a big difference between internal/external expectations and having to work a high stress job to afford food.