At NewYork-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.