Bbart, your last post is a bit odd. Do you think you might have some facts confused?
Julies198 expressed concern about the marriage of Catherine Armstrong to William Ridley Dixon. I am agreeing that it appears it is NOT for the Catherine Armstrong/Dixon, mother of William Armstrong, as William Armstrong appears to belong to the "Lanercost Armstrongs", not the "Shaddongate Armstrongs".
If your concern is regarding the John Armstrong with the Watsons, that is based on the scrap of a marriage that William Armstrong had in his possession. It appears to be a match for a marriage of a Catherine Dixon marrying a George Andrew Watson, and looking at the 1901, 1911, and 1921 census' for this couple, they have Catherine's brother John, living with them. Catherine and John's ages and birth locations do match that of the Lanercost Armstrongs' where you found William born Scotland.