Being connected to the Stanhope family myself, I was interested to check his tree, but dissapointed to come across an error. His Mary /Margaret Jerningham who married Thomas Stanhope would appear to be the daughter of John Jermingham and sister of Edward Jermingham who married Mary Scrope. As his tree was supposed to ascend through Mary Scrope up to William the Conqueror, if what I found is correct, then he would not be a direct descendant. I would be happy to be proved wrong!
If this is indeed correct (I have not had time to fully check) then he seems to still have a descent from Henry II anyway and thus back to Guillaume "le batard". This connexion would be via Stanhope, Talbot (Elizabeth Talbot married John Stanhope, of Rampton, father of Thomas Stanhope who married Mary Jerningham), (de) Holand, (de la) Zouche and (de) Longespée.
I noticed Tracy was one of the surnames in his ancestry as well (I am a descendant of this family but via their English branch, rather than their later Irish one).
He also appears to have a descent via Burdett, Tracy, Devereux, Grey, Ferrers, Mowbray and therefore to Henry III.
He likely has many others as well. They presumably chose this particular descent from William I, over those others, likely due to the story of Sir Michael Stanhope.
As for descent from William I., I have many descendents from him due to being a two-time descendant of Edward III. Once one finds a Gateway ancestor it is not so difficult to trace lines back into mediaeval times (although records need to be checked carefully, especially Heralds Visitations) and in some regards back to the British monarchy.
The Rolleston/Rolston family are also a relatively well known gentry family, so it makes tracing his ancestry not that much difficult.
Even without the links back to Henry II, Henry III and/or William I, I appear to be a very distant cousin of Frank Gardner (as I am of many thousands of individuals) via the Tracy family.
I did find the programme very interesting though due mostly to the fact I share some ancestry with him (but not via Sir Michael Stanhope).