Dr. Thomas R. Frieden, director of the C.D.C., had publicly stated that because Ms. Vinson was being monitored for possible exposure to Ebola, she should not have flown on the return flight. His comments suggested that the fault lay with Ms. Vinson, but it has become clear that Ms. Vinson had checked in with health authorities.

Asked if Ms. Vinson was owed an apology, Mr. Jenkins replied: “Amber Vinson did nothing wrong. To the extent that it would help her family in healing, on behalf of the joint team — one team, one fight — and the decision makers who made that decision, I apologize for us.” He later said he was unaware Ms. Vinson had requested a private plane.

In Dallas on Monday, no one was underestimating the seriousness of the disease, which has led to more than 4,500 deaths in Africa and continues to pose a potential risk to those being monitored in Texas and beyond. But while some of those on the edges of the three Ebola cases have worried about exposure, the end of the monitoring period on Monday for some of those who saw, lived with and touched Mr. Duncan was a reminder of Ebola’s mysteries and misperceptions.

“It speaks to the fact that while Ebola is scary, it’s not that contagious,” said Dr. Amesh A. Adalja, an infectious-disease specialist in Pittsburgh. That Ms. Troh in particular did not become infected has astonished many given that she and Mr. Duncan shared a bedroom while he was symptomatic. She had spoken of caring for him while he sweated profusely, had a fever and suffered from diarrhea. Ebola is not an airborne illness, but it can be transmitted to those who have direct contact with the bodily fluids of a symptomatic victim.

“She is very lucky that whatever her exposure was the virus was not able to transmit to her,” Dr. Adalja said, adding that researchers were studying whether a person’s genetic makeup might make him or her less susceptible.