So, the real confusion has been between Col. William Ball and William "Assumed Ancestor" Ball, no? They just both happened to have a son named Richard who lived in Virginia.
The postulate you posted seems eminently sensible, given that, although I don't know anything about the spawn (or lack thereof) of Elizabeth Linton. But it is consistent with this:
"Others have put forward Richard Ball and Elizabeth Linton as the parents of John Ball. The father of Elizabeth Linton was a Moses Linton of Lower Norfolk Co., VA. Richard Ball and Elizabeth with several Lintons moved to the Fairfax-Stafford county area from Norfolk Co. At this time, there is no known record evidence which links Richard Ball and Elizabeth Linton with John Ball."