However, Customs and Border Protection Los Angeles spokesman Jaime Ruiz told the Herald the passenger was refused entry to the United States because he was drunk and verbally abusive to crew and passengers on the flight.
"He was returned to New Zealand. He wasn't violent, there's no crime, no charges, he was just denied entry to the US."
An Australian passenger told the Herald the incident unfolded about four hours into the flight - roughly a third of the way through the journey.
"A man was knocked to the ground by staff and tied up to his chair for the rest of the flight.
"It looked like they used seat belts to hold him to the chair. The crew wouldn't say anything and most people didn't know it happened. The crew did a great job and really took care of it."
The man was tied up at the very back of the plane, the passenger, who did not want to be named, said.
"When we got to LA they had eight police officers waiting at the door to come in and remove the man. They also made us get off the plane away from the main airport.
"Seeming it took five staff to get him down they were worried about getting him off. I was talking to the guy next to me and he said it was very odd how far away from the main airport they put us. It was a good 15-minute bus ride and there was nothing around us."
However, the Air New Zealand spokeswoman said their crew were trained in restraint procedures, which could include lowering an unco-operative passenger on to the floor.
"This customer was not knocked to the ground as suggested [by the other passenger]."
She also said the plane was directed to a remote gate, and passengers then bussed to the terminal, because the flight landed in Los Angeles 20 minutes early and its allocated gate was not yet available.
The FBI has jurisdiction over incidents which occur in the air on United States-bound flights.
The Herald has requested comment from the bureau's Los Angeles office, but has not yet had a response.
Yesterday, a domestic Air New Zealand flight had to be aborted on take-off after striking a bird.
Auckland-bound flight NZ402 had 148 passengers on board when the incident happened on a runway at Wellington Airport about 6.30am.
The plane is understood to have braked sharply as it attempted to take off after striking the bird.
An Air New Zealand spokeswoman said the plane returned to the gate where it was inspected by engineers before departing 40 minutes later.
