My understanding: My Fair Lady had been a huge stage success, starring Julie Andrews. But when it came time to cast the movie version the producers, seeking the box-office appeal of a "star" name, passed over Ms. Andrews and selected Ms. Hepburn -- who unfortunately cannot sing. The difficulty was resolved by having her songs dubbed ... by Ms. Andrews.

Which hardly seems fair to the original fair lady.

Ms. Andrews, however, had the last laugh. Not being occupied with the production of My Fair Lady, she was available to take the lead in another movie, which proved rather successful: The Sound of Music.

Edit: Sparteye, below, is correct in her correction.