Consider for a moment that none of your ancestors had their DNA tested. Your DNA can only suggest a connection with somebody else who had their DNA tested when certain relatively conserved areas are identical. If it is Y-chromosomal DNA this suggests that the two individuals had a patrilineal ancestor in common, if it is mtDNA it would be a matrilineal ancestor. It does not indicate who the ancestor is, that can be inferred from pedigree charts. If both individuals had John Doe in 1650 as a paternal ancestor it is very likely that he indeed is their common ancestor. Disproving ancestry on the other hand is certain: If two people have the same paternal ancestor in their pedigree but their Y-chromosomal DNA is different it is certain that one of them is mistaken in their belief in a biological relationship.