One very strong interpretation would be that as an altruist experiencing life unencumbered by religious morality, he still has to experience and make sense of why there is suffering in the world and how it relates to his choice to find meaning. In a theological sense, God answers all those questions, but to an existentialist, one must select one's meaning and make sense of suffering without a story such as the devil. This quotation is just an observation that Rieux has seen people suffer collectively, he doesn't like it, and he certainly wouldn't endorse the use of collective punishment. Remember, his meaning is derived from his ability to heal and mend people and allievate their suffering.
In The Plague by Camus, one of the central characters is Dr. Bernard Rieux. From the article:
Dr. Bernard Rieux: Dr. Bernard Rieux is described as a man about age 35, of moderate height, dark-skinned, with close-cropped black hair. At the beginning of the novel, Rieux's wife, who has been ill for a year, leaves for a sanatorium. It is Rieux who treats the first victim of plague and first uses the word plague to describe the disease. He urges the authorities to take action to stop the spread of the epidemic. However, at first, along with everyone else, the danger the town faces seems unreal to him. He feels uneasy but does not realise the gravity of the situation. Within a short while, he grasps what is at stake and warns the authorities that unless steps are taken immediately, the epidemic could kill off half the town's population of two hundred thousand within a couple of months.
During the epidemic, Rieux heads an auxiliary hospital and works long hours treating the victims. He injects serum and lances the abscesses, but there is little more that he can do, and his duties weigh heavily upon him. He never gets home until late, and he has to distance himself from the natural pity that he feels for the victims; otherwise, he would not be able to go on. It is especially hard for him when he visits a victim in the person's home because he knows that he must immediately call for an ambulance and have the person removed from the house. Often, the relatives plead with him not to do so since they know they may never see the person again.
Rieux works to combat the plague simply because he is a doctor and his job is to relieve human suffering. He does not do it for any grand, religious purpose, like Paneloux (Rieux does not believe in God), or as part of a high-minded moral code, like Tarrou. He is a practical man, doing what needs to be done without any fuss, but he knows that the struggle against death is something that he can never win.
Cliff's notes also has an analysis of this character:
The narrator is about thirty-five years old. He is a highly respected surgeon, but Tarrou thinks that he might pass more easily for a Sicilian peasant. For example, Rieux's hands are not long and sensitively surgeon-like, but broad, deeply tanned, and hairy. Rieux is of moderate height and broad-shouldered; he has dark steady eyes, a big, well-modeled nose, and thick, tight-set lips. His black hair is clipped very close.
He belongs to a small group of people whom Tarrou calls "true healers." While there is still time for him to leave Oran and join his wife, he refuses. He remains in Oran to fight the plague with all his talent and strength. There is nothing heroic about his actions. He fights death and disease because he has been trained to and because he conceives of his life having value only when he is continuing to help others combat death and achieve health. There are only two evils for Rieux — death and man's ignorance of it.
About his personal relationships with his wife and mother, Rieux has misgivings. His love for mankind is consummated daily, yet to those for whom he is husband and son, he feels that he is probably inadequate. During the plague's last stages he regrets not giving more physical and vocal affection. Rieux's flaws, including his exhaustion and his tears when Tarrou dies, are necessary for a correct interpretation of his character. He says in the chronicle that he has told only what was experienced by all, that he has not made the book a highly personal confession. He does not separate himself or his duty from that of every man. Rieux tries to be definitely human — no more, no less.
Thus, in this novel, one might consider Dr. Rieux an example of a Jungian archetype, the Caregiver. Caregivers are often invoked in narratives to embody principles of altruism, which is relevant in notions like deontological ethics. Remember, existentialism can be roughly understood as an individual on a mission to understand who they are and to take ownership of one's choices and ethics. This is one of the primary struggles after an individual, in this philosophical theory, has one or more existential crises.
As for the quotation:
I've seen too much of hospitals to relish any idea of collective punishment.
The good doctor has witnessed the effects of a plague, and thus experienced first-hand human suffering. Like any philosophically inclined athiest, even though he doesn't gravitate towards moral absolutism to handle the problem of evil, he still manifests empathy. So, having seen a group of people suffer collectively from disease, he carries that by analogy to the collective suffering of people at the hands of a punisher.
Addendum and Response to Philip the Klöcking's Comments
'Real' suffering? Well, that claim is fraught with ontological ambiguity. :D Let me thank you for the reference to Tomasello. His theory of ontogeny is a great evolutionary complement to 1) Searle's notions on human intentionality and the social construction of reality 2) de Wall's general ethological musings on great apes and their being, and 3) EO Wilson's writings on sociobiology and human eusociality. Let's draw from Tomasello...
Human sociality as Tomasello sees it is drawn largely from the shared intention of humans particularly "individual experience in such things as collaborative and communicative interactions with others, structured by cultural artifacts such as linguistic conventions and social norms." This is the pith of the social construction of reality, the "politics of experience" as RD Laing calls it. And one of the greatest contentions of shared reality is the nature of causality. An existentialist is freed from the very social norms of reality itself (let's say inferential constructions biased by one's Umwelt), and thus, must take responsibility for choosing the nature of causality. This theme, of course, goes back to Thales and the debate between theologi and physiki in Anatolia, and extends through Aristotelian thinking right through the Scholastics right up to modern times. As a self-avowed absurdist, Camus, it would seem to me takes it one step further and not only declares God dead in the Nietszchean sense, but claims that one can't even fundamentally choose a meaningful existence in the broader sense. One can choose one's meal, but one can't choose to have a meaningful existence.
Is The Plague (in Aristotle's language), a material cause or is it a formal and efficient cause culminating in a final cause? An existentialist must wrestle with the terror of freeing themselves from the social norms that promulgate the latter. In the story, Paneloux is a champion of God's Providence, but whereas an existentialist by nature must reject Providence to assume responsibility, an absurdist must reject that there is even a choice in meaning. It is possible to be a Christian and an existentialist. But this is not true of absurdism or nihilism. Life simply is random and chaotic and no matter of existential suffering or crises resolved can imbue life with meaning.
A central motif of Western literature is the Christian God's use of plagues to punish mankind. Man, of course, emulates this when assigning group punishment (Roman decimation comes to mind). It's not a coincidence that Camus has Rieux make a connection between the oft-touted collective punishments of God and mankind's arrogance in emulating this. I don't think it's a coincidence to name the novel after the use of divine collective punishment, and then reflect on man's aspirations to use the same punishment in some way that purports to serve a greater meaning in society. It's obviously a commentary on "God's use" of the bubonic plague to instruct man on matters of reality, character, and faith. Ultimately Paneloux in his delusion to spread God's will succumbs himself to the random vagaries of illness.
Ultimately, to an absurdist, all human suffering and death are the result of material causes of existence with neither rhyme nor reason, not in the proximal sense, but the distal one.