Move your argument to 1940 and make it about the prospect for future treatments for heart disease to see how ridiculous it is to suggest that only the wealthy would have access to these medical technologies.
One of the interesting things about our age is that medicine is largely flat. Rich people can buy more time from more expensive physicians, and pay people to do their legwork and phone calls for them, and lie in pain in better-looking ward rooms, but there are very, very few forms of medical technology available to them that is unavailable to someone with a few tens of thousands of dollars and the time to make the phone calls and do the legwork.
Given that the treatments for human rejuvenation will be infusions (made up in a lab-factory in bulk, or a specialist clinical plant to order, and requiring very little attention from trained staff to administer) rather than surgeries (requiring a great deal of time from specialist staff to carry out), I think that the odds of their remaining expensive for long are minimal. Economies of scale emerge rapidly for such things.
(Infusions because these treatments will be things like delivery of engineered bacterial enzymes, gene therapies for mitochondrial DNA, drugs to break down cross-linked proteins, stem cell transplants, and so forth).
Look at stem cell transplants as the model of how the price of such therapies rapidly moves downward due to inter-regional competitive pressure for treatments of this nature.