Hi John,
Although you made mild fun of Roger's comment about 'Feeling', I think he hit the nail square on its head! Without being able to express yourself and put feeling into any piece of music you may play, you might as well just use some kind of mechanical method - such as a player piano - to play the music. There is a world of difference between sitting down and playing a piece of music absolutely 'note perfect' from the score, and playing one's own interpretation of the written part, by adding these little personal nuances, phrasing, light and shade etc. without actually departing from the written melody. Adding improvisation is of course a whole new ballgame.............
Your comment "...
Take the music away and she stopped playing..." says it all - I have come across quite a few musicians like that. However, I have also met many who are very good readers, but were able to play their own interpretation of the written score and add that certain indefinable 'Feeling' to their performances.
I believe that a sense of Rhythm is something which is born in us - some have it - some don't (the unluck ones!) and I am of the opinion that it cannot be taught. A similar gift is a natural sense of harmony. Harmony can be taught in an academic sense, but to 'Feel' it naturally, is totally different. You only have to listen to a gathering of native Africans singing and dancing - I very much doubt if they ever had any lessons in Rhythm or Harmony

I count myself very lucky to have been blessed with a good sense of rhythm and also a natural sense of harmony, and I firmly believe that I inherited these gifts from my parents and all four grandparents, since they all played musical instruments.