I'm afraid her story cannot be 'reconciled' with the proven facts. [=her story must be false because it does not agree with the proven facts]
After many years, they 'are' finally 'reconciled' (with each other). [=they are friendly again]
His attempt to 'reconcile' his friends (with each other) was unsuccessful.
(..) ...especially this late in the game. My father talked about things he never did... ...and I'm sure he did a lot of things that he never talked about. I'm just trying to reconcile the two. The first thing you have to understand... ...is that your father never meant to end up here. Yet he did. (..)2003 Big Fish