This is a dangerous trait for a leader. On the surface, Biden believes that he really did visit that synagogue. And his mind refuses to venture below the surface. His mind's greatest fear is the exposure of 'truth' that would contradict his view of the world, a view where he is so deserving of praise because he visits synagogues.
LBJ had a similar problem. He repeatedly told the story of how his grandfather died at the Alamo. This defined his suitability as Commander-in-Chief and justified his authority for speaking on the radio directly to bomber pilots during their missions over Vietnam. His deception about his grandfather translated into half a million young men being sent to Vietnam over the course of his five years in office.