The Man from Earth

The film begins with Professor John Oldman (David Lee Smith) packing his belongings onto his truck, preparing to move to a new home. His colleagues show up to give him an impromptu farewell party: Harry (John Billingsley), a biologist; Edith (Ellen Crawford), an art history professor and devout Christian; Dan (Tony Todd), an anthropologist; Sandy (Annika Peterson), a historian who is in love with John; Dr. Will Gruber (Richard Riehle), a psychiatrist; Art (William Katt), an archaeologist; and his student Linda (Alexis Thorpe).
As John's colleagues press him to explain the reason for his departure, he slowly, and somewhat reluctantly, reveals that he is a prehistoric caveman who has lived for more than 14 millennia, and that he relocates every ten years to keep others from realizing that he does not age. He begins his tale under the guise of a possible science-fiction story, but eventually stops speaking in hypotheticals and begins answering questions from a first-person perspective. His colleagues refuse to believe his story. John continues his tale, relating how he was a Sumerian for 2000 years, a Babylonian, and eventually went east to become a disciple of Gautama Buddha. He claims to have been given a chance to sail with Christopher Columbus (admitting that at the time he still believed the earth was flat) and to have befriended Van Gogh (one of whose original paintings he apparently owns, a gift from the artist himself).
In the course of the conversation, each of John's colleagues questions his story based on knowledge from his or her own academic specialty. Harry, the biologist, struggles with how biology could allow for the possibility of a human being living for so long. Art, the archaeologist, questions John about events in prehistory. He exclaims that John's answers, though correct, could have come from any textbook. Will, the psychiatrist, questions if John feels guilt for outliving everyone he has ever known and loved, and threatens John with a gun (which ends up being unloaded) before temporarily leaving. John then learns from the group that Will's wife had died the previous day after a long illness.
The discussion turns to the topic of religion. John mentions that he is not a follower of a particular religion; though he does not necessarily believe in an omnipotent God, he does not discount the possibility of such a being's existence. Pressed by the group, John reluctantly reveals that, in trying to bring Buddha's teachings to the West, he became the inspiration for the Jesus story. After this revelation, emotions in the room run high. Edith begins crying. Will demands that John end his tale and give the group a sense of closure by admitting it was all a hoax. John appears to ruminate over his response before finally apologizing to everyone for leading them on.
John's friends leave the party with various reactions: Edith is relieved; Harry indicates an open mind. After everyone but Will and Sandy has left, Will overhears John and Sandy's conversation, which suggests the story was true after all. John mentions some of the pseudonyms he has used over the years, and Will realizes one was his father's name. Shocked to realize the ageless man is his own father, Will suffers a heart attack and dies. After Will's body has been taken away, Sandy realizes this is the first time John has seen one of his grown children die. John wordlessly gets in his truck and starts to drive to an unknown destination. Then he stops and waits for Sandy, who walks over to the truck.

Question: What does John claim?
Answer: to have been given a chance to sail with Christopher Columbus