it is my story because i am trying to convey my thoughts, emotions and perspectives by capturing one moment in time of the subject. Like what wolfgang says, it will be tainted by my own prejudice, my view of the world, etc.
it is at the same time the subject's story because clearly, it's about the subject and his/her view of the world albeit it is his/her moment captured.
it is also the stories of the viewers/observers of the image. How they see the story depends on how they relate to the subject's and photographer's story. How they see it may not be how the subject sees the story or how the photographer sees the story.
This is the beauty of the image. The interlink and inter-relationships shared by 3 people tied to that particular moment in time.