This story reminds me of the rumor about Eddie Van Halen meeting John Bonham at the Rainbow, rumors of suggested legal pressures by Chris Dreja's legal representation, Jimmy Page attending tour dates of the Jeff Beck Group's second tour, the discussion on when and where Jimmy Page recorded on Heart of Stone, and rumors about Mars chocolate bars, the Rolling Stones and Marianne Faithfull.
It's one of those stories that resurfaces every so often, that may or may not have had its origin in the Sun many moons ago. Those kinds of stories are self-perpetuating. So far it appears the songs by Jackie DeShannon and Jimmy Page were written in London, and the tale about Los Angeles appears to be somewhat mythological, as usual. No one ever proves these storeis, and yet they keep coming back.
Jackie DeShannon was in Los Angeles in 1964. Andrew Loog Oldham was in Los Angeles in 1964. I remember Jimmy Page being around Los Angeles in 1966.
Come And Stay With Me was one of Marianne Faithfull's early songs.
My Time of Sorrow was a lesser heard song.
http://www.youtube.com/watch?v=5JRv6iCCYQocould really sing, but she could dance the jerk and wore really cool skirts, too.
So Jimmy Page was recording in London at Regent Sound and Decca in June and July, 1964. Also, there is no mention of Jimmy Page playing in Los Angeles in November when the Stones recorded the next version of Heart of Stone.
As late as August-September, 1964, Jimmy Page was still recording in London. Jackie DeShannon was touring with the Beatles in 1964.