Was "Beautiful" really pitched to Pink? 

I have a problem with the caption below Pink's photo "Originally, the song was initially pitched to Pink"; from what I've heard on TV specials, interviews, and such, of Linda and Pink... the song was never pitched to Pink, she heard it before simply because she was working with Linda, but Linda never meant for Pink to get the song. In fact, Linda wanted to record the song herself, and changed her mind only after hearing Christina sing it in the "Stripped" sessions, which was, if I'm correct, moths after "Misunderstood" was finished.