‘An NYU Dump’ In the summer of 2021, a few months after Dr. Femia’s presentation, an ambulance dropped off a disheveled homeless patient at NYU’s emergency room. He had pain in both legs and was having trouble walking.

A worker checked the man’s vital signs. He was offered Tylenol and discharged, according to an email that a senior nurse later sent to more than 200 colleagues detailing what had happened.

About an hour later, the man was back. This time, he was seen in the waiting room by a social worker, who noted that it was hard for the man to lift his legs from his wheelchair. No one undressed the patient to examine his legs. He was discharged again.

It was not until later that day that the hospital admitted him. The man was diagnosed with acute kidney failure and rhabdomyolysis, a potentially fatal muscular condition.

Ms. Greiner said the case had been handled appropriately. But medical staff noted that NYU included it in an internal review process in which doctors try to learn from mistakes.

Doctors and nurses described a pattern in which homeless patients — surefire money losers for hospitals — sometimes received cursory care, even as privately insured patients with similar symptoms were admitted for urgent treatment.

For poor or homeless patients, “there is pressure to see them in the hallway or in the waiting room,” said Dr. Jeremy Branzetti, who ran NYU’s emergency-medicine residency program until last year. “I have never seen a V.I.P. patient in the hallway.” Mr. Phillips, the lawyer for NYU, said Dr. Branzetti had received a poor performance review and his contract was not renewed.

Some homeless people struggle to get into NYU’s emergency room in the first place.

Anthony Almojera, the vice president of a union that represents emergency services officers, said nurses at NYU reprimanded ambulance crews when they tried to drop off patients who appeared homeless or intoxicated.

“I had instances where the nurse’s first question wasn’t ‘What is wrong with the patient?’ but ‘How come this patient is being brought here?’” Mr. Almojera said.

Another ambulance worker, who requested anonymity because he still works with NYU, said that when he tried to drop off a drunk patient in October, a nurse demanded to know his badge number.

The pressure from nurses works: Paramedics who work on public ambulances said that instead of taking drunk or homeless patients to NYU, they routinely dropped them off at Bellevue, which is staffed in part by NYU residents.

NYU’s own fleet of ambulances, which handle some 911 calls, also take their unwanted patients to Bellevue, according to four nurses there.

“There isn’t a day that goes by that we don’t get an NYU dump,” said Kim Behrens, who has spent more than a decade as a nurse at Bellevue.

“We treat undomiciled persons every day and give every effort to do so with dignity, respect and compassion,” Ms. Greiner said. She also pointed to data showing that NYU treats thousands of Medicaid-eligible patients.

Accreditation in Jeopardy

By 2021, doctors had lost patience with the administration’s elevation of V.I.P.s, which they saw as unethical and dangerous to other patients. Some quit. Others complained to hospital administrators.

Then the Accreditation Council for Graduate Medical Education, which oversees medical training programs nationwide, received an anonymous complaint. One of the four allegations was that the V.I.P. system “teaches residents patient bias,” according to a letter the council sent to NYU in November 2021.

The accreditation council interviewed more than 50 doctors, who confirmed that V.I.P.s were regularly given priority. Citing Dr. Carmody’s ouster, they described being afraid of professional consequences if they did not give preferential treatment to well-connected patients.

The council said that climate of fear violated the group’s educational standards for medical residents. And the organization said it was unclear if NYU had taken steps to ensure that the V.I.P. process would not harm patients.

In August, the council put NYU’s emergency department on probation, jeopardizing the accreditation of its residency program. It was a rare move: Last year, of 12,740 residency programs, just 25 were placed on probation.

NYU has two years to address the council’s concerns. Losing the accreditation could cost the hospital millions of dollars a year in federal funds and doom the residency program, which the hospital relies on to keep its emergency room running.

Ms. Greiner accused the accreditation council of recycling “false” allegations about V.I.P. patients getting special treatment. The council said it stood by its findings.

Susan C. Beachy and Kitty Bennett contributed research.