Indeed. But Occam's Razor only applies to a conclusion's relation to the information you have at hand. It is conceivable that if you collect enough information the same heuristic can lead you in a different direction.
It should be able to confirm his genetic relationship to his putative great-great-great grandchildren, and thus let a lower limit on his age. That and other documentary evidence of him and his descendants could make his age seem plausible. In a world with seven billion people, outliers can be very unusual indeed.