it isn't exactly my story -- it belongs to a friend of mine, so it may be exaggerated or apocryphal or an outright invention, but nonetheless, it makes me laugh, so I'll share it with you here.
It was the fall semester of 1990, and we were freshmen, newly freed from the bonds of high school and living with our parents. One of my friends was walking to the library one evening when an older priest joined her on the sidewalk. He struck up a conversation with her as they walked across campus, asking her about where she was from and how she liked Notre Dame so far.
As they entered the library, he introduced himself: "I'm Ted Hesburgh." My friend laughed, which led the priest to give her a quizzical look. They stepped onto the elevator and she turned to the priest, who joined her on the elevator, and said, "Don't be silly. Everybody knows Father Hesburgh is dead."
The priest (who, of course, was indeed Fr. Ted) chuckled as the elevator rose. She got off on an intermediate floor, they said their goodbyes, and she didn't think much about it.
Later that night, she told her roommates this story. They were all aghast, and my friend asked, "What?" One of them said, "Uh, Fr. Ted is alive and well." They rummaged around and found a photograph of him and showed it to my friend, who squeaked and said, "Oh no, I insulted Fr. Hesburgh."
The next day, she went to the 14th floor of the library and asked quietly to see Fr. Hesburgh. The secretary replied that he was not there, and my friend said, "Well, yesterday, Fr. Hesburgh and I walked to the library together, and he told me who he was, and I said --" The secretary interrupted: "Oh, that was you! Fr. Ted couldn't stop laughing about that when he told me."