As above, the full body rowing thing you see everyone doing at the commercial gyms are the guys who look around to see who is watching while they 'row' with 200 or whatever pounds. Turning it into a back extension exercise doesn't help the mid to upper back very much.
You can imitate the heavy barbell row type of motions on a seated row pretty easily, and they are easier on your back, if its an issue. Sitting as upright as you can ( while keeping back arched) the whole time, mimics a Pendlay type row. Leaning back at about a 20-30 degree angle the whole time (again with back arched the whole time) mimics a bent over row motion. I guess you could also do these by staying in the same back position, and varying the height of the pulley.
The width of grip while rowing puts(a bit more) stress on the back in an inverse relationship. Meaning close grip hits the outer/lateral back (Lats, Teres) a bit more than inner, and a wider grip will put a bit more stress on the inner/medial back (rear Delts, Rhomboids and mid-lower Traps) as opposed to the outer. But any row hits all of these in at least some amount.