I t does seem to fit in with that quote of Brian's from the Thomas article - and the reported date was Valentine's Day, presumably as a song for Marilyn. But Alan has since confirmed that it is indeed from the Friends era. So what "me and piano" piece was Brian talking about? The only thing I can come up with is the tack piano version of the Bicycle Rider theme, which may have been recorded Feb 15. It's possible a With Me Tonight outtake could have been recorded at this time, but those outtakes have the Beach Boys on vocals.
I've always thought that the piano piece he was referring to is something that we've never heard of, lost to time or tape erasure.