In Elizabeth Hartline's book, she identified James Jolliff as the father of the James Jolliff (d. 1821) who married Elizabeth Norris and went to Kentucky, but hedged on James, Sr.'s father. Then, as far as I can see, there isn't any strong evidence regarding the parents of John Jolliff, the immigrant to Virginia (d. 1658). It does seem that he probably came from the Leek family, because (this is all from memory, so I might be mistaken) of the existence of the Bacon family nearby. But certainly the Elizabeth Skinner is wrong----according to what I recall from the British genealogy of that family, Elizabeth Skinner married Thomas Jolliffe, Esq., of Leek (b. c.1627).
I have my doubts that John, the immigrant, would be the John of Leek that she identifies, because he was illiterate, and the men in such a wealthy gentry family at that time would certainly have been able to sign their names.