Ever since the race to develop a coronavirus vaccine began last spring, upbeat announcements were stalked by ominous polls: No matter how encouraging the news, growing numbers of people said they would refuse to get the shot.

The time frame was dangerously accelerated, many people warned. The vaccine was a scam from Big Pharma, others said. A political ploy by the Trump administration, many Democrats charged. The internet pulsed with apocalyptic predictions from longtime vaccine opponents, who decried the new shot as the epitome of every concern they’d ever put forth.

At New York-Presbyterian Morgan Stanley Children’s Hospital, one of the most highly regarded hospitals in New York City, a rumor spread last week that the line for the coronavirus vaccine on the ninth floor was unguarded and anyone could stealthily join and receive the shot.

Under the rules, the most exposed health care employees were supposed to go first, but soon those from lower-risk departments, including a few who spent much of the pandemic working from home, were getting vaccinated.

The lapse, which occurred within 48 hours of the first doses arriving in the city, incited anger among staff members — and an apology from the hospital.

“I am so disappointed and saddened that this happened,” a top executive at NewYork-Presbyterian Morgan Stanley Children’s Hospital, Dr. Craig Albanese, wrote in an email to staff, which was obtained by The New York Times. ...