It does nothing of the sort.
Since it is exactly what you said, of course it does.
Plagues with massive rates of mortality are rare. In ancient times, and until just the past few hundred years, no one had any real idea about methods of transmissions, and obviously no access to the kinds of modern medicines and vaccinations which we know work.
Caring for someone had very little, if any, impact on mortality, other than exposing the caregiver to the contagions. People did care for one another anyway, and did so even when the only known Europeans were Neandertals.
Stark shows that a small amount of care could make a significant difference in mortality rates.
In Roman cities, as in many urban areas, there is more anonymity, less of extended families and coherent tribes.
People inside their extended families and tribes tend to care for one another much more than outside of their insiders.
People outside their families and tribes are most commonly only seen as enemies and/or prey.
Maybe Stark is wrong. He looked at it statistically and concluded a rise in percentages of Christians after epidemics.
Of course, evidence is sparse from 1900 years ago.
Stark was trying to answer the question: How did Christianity take over the Roman Empire.
This was one of several mechanisms he found plausible.
He also presented evidence that Christianity was the religion of middle and upper class Romans more than of the lower classes, at least early on.
It does nothing of the sort.
Since it is exactly what you said, of course it does.It is not exactly what I wrote, as you can see.
It only supposes that Christians were *more* willing to care for others.
That is built into Christianity, and it is considerably different than most other religions at the time.
It was almost the opposite of the major Roman ethos, which, I have read, feared becoming "weak" or "sentimental".
Sorry, I do not remember the source for that.