Though police and incident reports say McCurley took the 13-month-old girl Monday to the back of the plane after seeing her mother slap the baby with an open hand, McCurley said she only offered to hold the child and help calm her down. She said she did not "take" the girl away from her mother, though controllers on the ground may have gotten that impression when the plane crew, flying from Dallas to Albuquerque, reported the incident.
"I picked the baby up from her, and the baby quit crying," she said. Only when the baby's father asked if he could hold his daughter in the back of the plane did she leave the mother's side, McCurley said, contradicting police reports.
"We thought we could do something good and get them some help," McCurley said.
The baby then fell asleep after the father rocked her, she said.
The baby's mother told police she slapped the child because she was kicking, and she was trying to teach the child that kicking is wrong, according to a police report.
When Albuquerque police officer Dana Baldwin asked the mom about the slapping after the flight, she told her, "I haven't done anything wrong with my child. I popped her when she kicked me and that was it," according to Baldwin's written statement on the report.
The mother, Lee Ann Cid, told Baldwin, the assisting officer at the scene, that she only hit her child lightly on the leg to get her to stop kicking and crying.
"She's done this before when she gets tired and she'll slap me in/toward my face and stuff," Cid said, according to Baldwin's report. "I think it's because she saw my nephew do it. He slapped my sister in the face and I guess she thinks it's OK. And I'm trying to teach her that it's not. And if she continues to kick because she saw him do it, it makes it OK. And the only reason I popped her is so she knows it's not. 'Cause when she's screaming and she can't hear me say no, that's the only way I can get her to stop."
Albuquerque International Sunport police told ABC News Tuesday that McCurley took custody of the baby after the incident.
When the plane landed in Albuquerque, the family was met by police. A Southwest Airlines spokeswoman told ABC News the local authorities were called "out of precaution for the child."
The parents were questioned by police and released to continue to their final destination.
According to the report from Albuquerque police, the parents, Lee Ann and Joseph Cid, were arguing on the flight, trying to get their 13-month-old daughter to stop crying, when McCurley intervened.
"She informed me several passengers had reported that a female subject traveling with a baby and her husband had been observed striking the child on the face in an attempt to get the child to stop crying," wrote the reporting officer, Sgt. Ernesto Rojas, who responded with Baldwin to the scene.
"McCurley further stated she walked to the rear of the aircraft and observed the mother of the child identified as Lee Ann Cid strike the child with an open hand on the face in an attempt to get the child to stop crying. McCurley further stated the mother appeared agitated with the child and that the husband continued to yell at his wife to shut up due to her screaming at the child."
According to the police report, McCurley said the child had a black eye, but the parents blamed that on an uncle's dog.
"McCurley then stated she took the child from the mother due to her behavior and walked to the rear of the aircraft with the child identified as a 13-month-old female," said Rojas' statement. "McCurley then stated the father identified as Joseph C. Cid walked back to the rear of the aircraft, took custody of the child and stood on the rear of the aircraft until the child fell asleep."
Police said McCurley did the right thing, and said the parents were not abusing their daughter.
"I think it was a solid move from the part of the flight attendant to take custody of the child," said airport police chief Marshall Katz. "It neutralized the situation, it calmed everybody down."
Southwest Airlines representative Whitney Eichinger confirmed to ABC News that there was an issue on the flight, but denied accounts that the flight attendant took the young child from its parents.
"What you read about the flight attendant taking the baby is not the case. She did it as a 'Would you like me to bounce your baby for you?'" Eichinger said.
"The family on board was having an altercation and their young child was upset. Our flight attendant offered to the parent -- offered to hold the child on board. Our attendants do that from time to time just to soothe the crying babies because they are used to walking up and down the aisles."
When called for clarification, the Albuquerque Sunport Police maintained that the child was taken into custody by the flight attendant.
The incident took place on board Monday's Southwest Flight 879, which originated in Dallas and stopped in Albuquerque before continuing to Seattle.