Both the FAA and Air Transat disputed that on Tuesday, saying Flight TS 961 had been cleared to land in Miami but that the pilot chose to return to Cuba and its maintenance staff there.
The flight lost a large portion of its tail rudder 30 minutes into an overnight flight on Sunday between Varadero, Cuba, and Quebec.
None of the 261 passengers or nine crew members was injured, according to the airline, but passengers said they were knocked around as the plane had difficulties straightening itself.
Some passengers said the pilot announced he had asked to land in Fort Lauderdale, a city just north of Miami, but was told that he wasn't allowed to because of the U.S. embargo against Cuba that doesn't allow commercial flights between the estranged countries.
''I was afraid of dying,'' Danielle Gagnon told The Associated Press by telephone from Quebec city on Tuesday. ''I thought it was over, but at least I was with my daughter.''
FAA spokesperson Laura Brown told the AP on Tuesday that the pilot contacted the traffic control center in Miami and asked to land in Fort Lauderdale, but was directed to Miami, where customs would still be open late at night and able to handle the flight.
The pilot did not declare an emergency and chose to return to Varadero, a decision made by the pilot and Air Transat control center ''because the company has access to maintenance staff at this airport,'' the charter airline said in a statement Monday.
''It is untrue that American authorities were opposed to allowing the plane to land on their territory,'' the company said.
Brown said declaring an emergency would have permitted the plane to land wherever necessary, but added the pilot probably considered he had enough control of the plane to return to Cuba.
The United States maintains a strict embargo on Cuba and no commercial flights are allowed into the United States. Canada has no such restrictions and is a major investor on the island nation, a preferred sunny spot for winter-weary Canadians.
Brown insisted Tuesday that the origin of the flight was not important and that the plane was directed toward Miami only because customs would still be open.
Gagnon said she was sitting in one of the last rows and heard a loud noise. As the plane's navigation struggled, the jet tilted and sent flight attendants falling.
Gagnon said the passengers were stunned when the pilot announced the plane could not land because ''Americans and Cuba don't agree with each other,'' she quoted him as saying.
Other passengers have recounted a similar scenario.
''We were outraged,'' Gagnon said. ''It could have been a planeload of Cubans and it changes nothing. We're still human beings.''
Several of Air Transat's Airbus planes were temporarily grounded after the incident. All company A310s were inspected and no problems were found, the company said. The damaged aircraft was put into service in 1991 and had been inspected only last week.