Hi Sweetie... :)
I heard the story a TAD differently. When director George Cukor cast Audrey in film MY FAIR LADY, she was told she would have to be dubbed due to incredible vocal range of role.
Hepburn thought that wasn't necessary, citing her vocal work in films FUNNY FACE and BREAKFAST AT TIFFANY'S. (Remember "Moon River"?)
Anyway, Hepburn INSISTED on recording score to prove her point. After listening to her tracks, Cukor (as well as Lerner & Loewe, authors of the score) were FULLY convinced she could NOT handle adequately the full singing range required for Eliza Doolittle role.
So, over her objections, Nixon was hired to dub her.
"I say YOU'RE the CUTEST one. No, I say YOU'RE the CUTEST One. And we go on like that from dawn to three."