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.
(..) Scully! In light of your report and narrative, my official report is incomplete... ...pending these new facts I'm being asked to reconcile. Though it seems that a federal agent may have been involved in the bombing... ...the other events you've laid down are too incredible on their own... (..)1998 The X Files