Marilyn Monroe was driven not only to be successful, to also to be a skilled and respected performer; consider her decision to leave Hollywood for New York for a while to study at the Actors Studio, which was widely ridiculed at the time.

I wouldn't be surprised if she learned those guitar chords specifically for that part, and learned them well. I've always assumed she was really playing the uke in "Some Like It Hot"; I'll try to watch more closely next time and make sure. One thing is very clear: she does her own singing in most if not all of her films, employing an unconventional but highly expressive and endearing vocal style.