My two cents: If you ride position is fully upright, core strength makes little difference unless you are MTBing. If you are rotated, it may make a significant difference. Yoga can get you there, it's doesn't mean doing classic sit-ups
http://www.youtube.com/watch?v=Ih0hZOeTfj4
The only time I have experienced back pain is riding on tourer that I have set up with a pretty high front end and a B17, I'm upright most of the time. A lot of strain and impact on the lower back, imho.