Should the upper body move forward and backward during the seated cable row?
I was watching instructional videos and found both styles, e.g.
Which one is right, and why?
They both are correct, although the one with Coleman where he moves slightly doesn't really add much, and does add slightly higher risk.
The theory is that by leaning forward on the eccentric phase you can get a greater stretch on the lats, and thus a better exercise. However, what you are really doing is simply changing the angle of the upper arm in relation to the upper body, and getting slightly more activation out of the lower back muscle groups.
If you watch carefully, the arms don't really start pulling in the Coleman video until his back is almost straight again, and they end in the same position, with upright back, shoulders pulled back tight, and elbows close so the grip is snugged in against the body.
The main differences is that by allowing the flexion forward, you can get an increase in the momentum of the weight, as it is already moving by the time your arms get into the act. If you are going for high weight, this can help, but it does increase the risk of injury because of increased activity/strain on the lower back. Assisted higher weight exercises and strict form exercises both have their place/uses, definitely what you want to avoid is going past vertical away from the weight stack in either instance.
I would do a weight that you know you can keep your posture as straight as possible. If your entire body is jerking too and fro, you won't be putting as much tension on the muscles, middle back, lats, biceps, and you will start incorporating "helper" muscles or nearby muscles to help you complete this movement.
Isolation and good form will yield better results than poor form and creating a compound movement out of something that should remain, well significantly static.
