Not claiming that my research can't have it's flaws, but from what I have found and supported by Burke's Peerage, etc. The stories above are NOT correct.

As I understand it:
William, 1st Marquise of Annandale and Earl of Hartfell (1663/63-1720/21) was married twice, 1st to Sophia Fairholm, by whom he had 2 daughters Henrietta and Mary and 3 sons James, John, and William. He 2nd married Charlotte van Lore van den Bempde by whom he had 2 sons, George and John.

William, the 1st Marquise died 1720 and his eldest son by his first wife, James became the 2nd Marquise. James died unmarried in Naples, Italy in 1730 (there is no account of him being insane) His younger whole brother John had died in 1694 and his whole brother William died 1721, so the title passed to James' oldest half brother George who became the 3rd Marquise. George's younger whole brother John died 1742 and his death may have contributed to George's mental instability. George was declared insane in 1748 and the management of the large estate turned over to three unscrupulous men who stole all they could from it. Despite their best efforts, when George died in 1792 the estate was still quite large and declared "in abeyance" until it could be determined who was the nearest kin and therefore the heir. There were many contenders for this title and the huge fortune that went with it for over 200 years. Eventually the courts decided that upon examination of newly discovered documents that although the Marquisate could not pass through a female line, the Earldom could do so. A grandson, John, of Lady Henrietta Johnstone (who had married the Earl of Hope) was granted the double Earldom of Annandale and Hartfell. He assumed the name of Hope-Johnstone and it is from this line that the current Earl descends.

There is of course the "legend" that William who was the son of the 1st Marquise and Sophia Fairholm did not die in 1721 but that instead he had quarreled with a favorite of the King's guard and killed him in a duel and that William's death was "faked" by his "mother." I have never seen any proof for this account and the fact that his mother, who is supposed to have helped faked his death in 1721 had already died herself in 1716, makes it hard for me give it much creedance. But of course, such stories die hard and many will continue to believe them.