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.
(..) Relationship with his father is worse than we imagined. This helps us how? The stronger the issues, the more powerful the catharsis. - How are we gonna reconcile them? - I'm working on that. Work faster. The projections are closing in quick. We gotta break out of here before we're totally boxed in. (..)2010 Inception