Family stories, like the old parlour game Chinese Whispers, do not pass through the generations and emerge unscathed: they are usually embellished, or assumptions are made which have little or no basis in fact. Certainly, in some cases there might be a kernel of truth lurking behind the inherited version and such stories should be explored rather than ignored or simply accepted as gospel.
The incentive for numerous people to begin researching their family tree is that they've heard they descend from a famous - or infamous - historical personage. Frequently the foundation is simply a shared surname - Nelson, for example. The truth is that Nelson had no legitimate descendants, his line being continued through his illegitimate daughter, Horatia. There are descendants through collateral lines.
While on the subject of Nelson, it has become a joke in genealogical circles that if all the ancestors believed by descendants to have served on the flagship Victory at the Battle of Trafalgar had TRULY been on board, the ship would have sunk and history might have been written very differently.