I think Mary does not claim to be free of this failing simply because she does not understand that she is not. It seems an odd thing to say without any qualification at all (eg, 'I know I am sometimes guilty of this', or, 'I, of course, could never be accused of behaving so') unless the speaker is completely unaware of their own tendancy to display that fault. I think it reveals Mary's complete lack of self-knowledge, and, therefore, is even more ironic!