I do believe that Fred's thinking has evolved over time on this point. When I attended the instinctive shooting clinic at BW several years ago, pivoting the body to bring the shoulders into allignment was not a part of the course. Now he says it is practiced during the course.
I learned pivoting the body from our own Terry Green, in his posts and video. It has made me a much better shooter to have my shoulders in the same allignment for each shot, regardless of where my feet are, and a better hunter to not have to worry about moving my feet around to get them into any particular allignment.
Fred favors keeping the shoulders slightly open, whereas Terry favors having the shoulders square to the target. I have always struggled with getting my shoulders completely square with the target. Since reading the TBM article, I have been experimenting with leaving my shoulders a little open. My feeling is that if the position of your shoulders is repeatable, you should be just as accurate one way as the other. I feel a little more relaxed with my shoulders slightly open, and as Fred says, it does seem easier to get my back muscles engaged. I believe my shoulder position is repeatable, since I bring my shoulders into as square a position as I can without any undue stress; when the undue stress starts is where I stop. But I haven't tried this long enough to be sure of anything yet.