Commentator Gary Gerani makes the same observation of its inappropriateness and yet continues to consider the film one of the greatest of all time. He's able (as are many) to overcome the dramatic license and enjoy the drama of the piece. Others like you can't. I'm sorry.
I also want to add that the Criterion Blu-ray of the film is still a valid part of the collection for this movie as it contains a completely different set of bonus features including the original 1954 television version. In an ideal world, one needs to own it and this new release, too.