The back story is only told from his point of view. So if he doesn't know, then it's not in the story.
If it's not an important story point to you, that you have something specific in mind, then go ahead and leaving it hanging for the GM to use or not use as they see fit. If there is something you have in mind, something you want to see developed in one direction or another, there's nothing wrong with adding an out-of-character footnote.