I say that having been at a screening in August of the movie, with Robert Morse there doing a Q&A. Might there have been discussions re: Rosemary singing "I Believe In You" before Lee signed on? Maybe and maybe Morse is only relaying what he understood or what she told him. But Morse specifically said that that was a condition from Lee of taking the part. (I'm linking an interview with Robert Morse re: that evening, although that comment by Morse is not in the article.) It was a wonderful evening and Morse is quite the raconteur. Also in the audience that night were several cast members who did the First National Tour with Morse.