Major humanitarian disasters challenge who we are. They provoke remarkable acts of humanity and the most terrible. In my career I've covered the aftermath of earthquakes, droughts and floods, including the aftermath of the catastrophe described in Sheri Fink's Five Days at Memorial – hurricane Katrina, which devastated New Orleans in August 2005.

The Memorial of the title is the Memorial Medical Centre where, for five days, staff and patients including a unit – run by a separate company – for terminally ill patients were cut off by the rising waters and by a city plunged into looting. Fink, a doctor turned writer, describes what happens when a health system run for profit by corporations is faced with making decisions relating to a wider public good.

At the book's heart is a dark and ambiguous story: the allegation that two doctors and several nursing staff working for the hospital on the last day of the crisis, awaiting evacuation, carried out euthanasia on a number of the terminally ill patients housed in the separate unit inside Memorial.

For Fink – who won a Pulitzer as a reporter for her investigation into what occurred at Memorial – the hospital was a "microcosm" of the larger failures that assailed New Orleans during Katrina, "with compromised physical structure, compromised operating systems, compromised individuals. And also instances of heroism."

By the time the crisis was over, 45 patients would die including 20 who were found with elevated levels of a cocktail of painkillers. Although the doctors insisted that they had been giving palliative care to the very sick, many of whom, they argued, were dying  after spending five days trapped inside the hospital, key personnel, including Dr Anna Pou and two nurses, Cheri Landry and Lori Budo, would later be accused of killing those patients,  though a grand jury refused to indict them.

Fink's story is, in too many grim aspects, a tragedy foretold. Hospital emergency preparedness in post-9/11 America, as she points out, was skewed towards terror, not natural disasters – particularly absurd in the case of the Memorial, which had been flooded before, during a hurricane in the 1920s.

"By 2005, more than a billion dollars had been made available to the nation's roughly 5,000 hospitals to promote bioterrorism preparedness," writes Fink. "Memorial's most detailed and by far its longest emergency planning scenario was written shortly after the 2001 attacks. This bioterrorism plan ran to 101 pages, as opposed to the 11 pages devoted to hurricanes."

In any case, what planning that had been done against a hurricane and flooding was half-baked. Despite a recognition that the hospital's key power plant was vulnerable to flooding, cost considerations had prevented it being placed somewhere more appropriate. Helicopter evacuation contracts were lacking and key decision makers at the health companies involved were both complacent and ill-equipped for what they had to confront. Instead, as disaster struck, trapping hundreds inside the hospital in grim conditions, the healthcare companies were left to busk it.

"Tenet [the company running Memorial itself] did not have pre-existing contracts with medical transport companies," says Fink. "The corporate headquarters did not have an incident command system in place for emergencies. One of its executives had served in the national guard and knew something about crisis management, but he was on vacation and offered tips by cellphone from a secluded beach retreat in Oregon."

Worse was to come. Inside the fetid hospital and at corporate headquarters, the two companies running the hospital and the terminal care unit not only failed to pull together, they worked against each other in planning evacuations by boat and in the often chaotic helicopter airlift from the roof.

What developed over the five days, in a hospital ironically well supplied with bottled water and food, and resupplied by air with drugs, was a system of triage that varied depending on which company had responsibility for the patients.

Against this background, it would later be alleged, key Tenet personnel discussed, and then carried out, euthanasia on the terminally ill patients even as relief was imminent.

Fink is in no doubt that some kind of crime took place even if she is fair and deeply sympathetic to the plight of the exhausted medical staff involved. "Moral clarity," she writes, describing the moment the patients were injected with a powerful cocktail of drugs, "was easier to maintain in concept than in execution."

If the beginning of the book is sometimes awkwardly structured, Fink finds her stride a few chapters in and make this a tight, provocative and gripping read.