Authenticity means truth to the soul: A person’s soul, the soul of an action or the soul of an idea. 
Sources
Important correction note: In the audio shiur it is implied that Ketura (Avraham’s latter wife –Hagar, according to chazal) was a a superficial hypocrite who had the external trapping but not the internal soul of her Jewishness. This is incorrect: The remark refers to the בני קטורה (sons of Ketura), not to Ketura herself.