Rita didn't actually sing 'Put The Blame On Mame'. It was sung by Canadian singer Anita Ellis who went uncredited. She actually rarely sang in any of her films. "Hayworth resented that the studio failed to train her to sing or to encourage her to learn how to sing. Although she appeared to sing in many of her films, she was usually dubbed. As the public did not know the secret, she was embarrassed to be asked to sing by troops at USO shows.".
Love Rita and love the article, but Fred Astaire was anything but an asshole! Rita, herself in a New York Times interview said, "I guess the only jewels of my life were the pictures I made with Fred Astaire.". He was actually known as the nicest and classiest guy in Hollywood as cited in many quotes by fellow actors, directors, producers and so on and so forth. Although he was a notorious perfectionist, he was also known to be very emotionally generous with everyone he danced with. There's even this story about Gene Kelly's behavior to Debbie Reynolds on the set of 'Singing In The Rain (confirmed by Debbie in interviews) "Another curious anecdote is about Debbie Reynolds. At the time of the film, she apparently was a gymnast rather than a trained dancer. Her lack of skills in the latter area enraged Gene Kelly into yelling at her at one point, after which she left the set to have a good cry under a piano on another set. Who should find her there but one Mr. Fred Astaire. Taking pity, Astaire decided to work with Reynolds to get her dancing up to snuff. After reading this story, I can't help but move ol' Fred a few notches further up the “hulluva guy” ladder.". The story was actually a lot worse, and Kelly even called himself an asshole for treating her the way he did.