Many years ago I heard Livingston Taylor at a wonderful club in Chicago called the Quiet Night. He was (relatively) unknown at the time - the name "Taylor" had just begun to emerge through his brother James' first post-Apple album - and the place was deserted except for a handful of us. He asked for requests(?!?), and a friend of mine from Virginia asked for "Dixie". He said he didn't do it and proceeded to play the most amazing version of it that I had ever heard, reminiscent of the Oh Susannah that James included on his afore-mentioned album. He has his brother's talent for finger-picking and for finding passing chords to support a song's melody - and he infused a lot of soul. He transformed the song from a march/rallying song to a lament and really touched the hearts of those present. In short, I learned that night that any song can turn out to be just right for the moment.
I've always felt that moments like that turn live performances into cathartic experiences. Although he may have dropped a word or chord here or there, that song meant more to us there that night than all the perfect technical recitations of his well-rehearsed repertoire.
Hope I haven't waxed too poetic. But I feel this relates to your question and to Neo's query about technique/soul (another thread), too.