There are many causes of back pain. If your back pain starts from muscle strain, reinforcing the torn muscle might help. However, tummy tucks do not generally help with back pain.
You've raised a very good question with regards to tummy tuck surgery. It is a point that I always cover with my patients pre-operatively. I am comfortable liposuctioning the flanks and mons pubis area during the tummy tuck surgery, but I am not comfortable with liposuction of the upper central abdomen (unless it's to create the median raphe only). I think it adds to increase risk of poor wound healing and potential tissue necrosis. For surgeons who can liposuction the mid-abdomen aggressively and not have a complication, I extend my admiration. But for patients and surgeons who have to deal with the resulting complication, it is a huge problem. So for patients with a thicker mid-section, I will often recommend a safer two-stage procedure. Three to six months after the tummy tuck procedure, return to aggressively liposuction the central abdomen, flanks, hips and/or back area. I wouldn't be too concerned about having loose skin again (of course, I don't have pictures to see). I think your surgeon made a prudent decision.