Well, I do not know for sure, but from other movies, it seems a few companies make jackets for a movie. Sometimes its a production company that make up the jackets from scratch ONLY for the movie (and no repro makers are involved).
If any repro makers did supply jackets for a movie, sometimes, they get screen time, sometimes they are worn by background extras, sometimes not used at all, but they ALL claim they made the jackets for the movie.
I know what you are trying to find, but its very difficult in this case unless either you contact someone from the production company or wardrobe dept... Or you get a categorical answer from either SMW or WW2 imp that their jacket was worn by Brad Pitt (even then they would also be more than one jacket, all the same). If they can't answer this simple question, then you have your answer.
If you are persistent that you want the SAME jacket that was used in the movie, then I would say continue to email the companies in question.
If you want a tanker jacket, because you like it, then get the best most comfortable one you can afford and patch it up yourself. It will still look great!