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.
(..) chosen from hundreds for her appearance, her grace, her poise... and her ineffable charm. We can never reconcile our differences. They are too elemental. This is no time to discuss our differences. Please, let's get this show on. Yes, the show! (..)1957 Funny Face