Well, my 6x great-grandmother, Catherine Arnold, wife of James Ballou, is apparently of unknown parentage, and is not the daughter of Elisha, although the book Ballous in America said otherwise.
I found the following in several forums; I assume as an effort to correct the record as much as possible--
Gary Boyd Robert's "Ancestors of American Presidents 2009 Edition", pg. 243 says:
"Catherine Arnold, born at Pawtucket, R.I. 28 Feb. 1690, daughter of Elisha Arnold and Susanna Carpenter, married Ebenezer Bates, not James Ballou, Jr.".
His sources for that are E.S. Arnold, "The Arnold Memorial" (1935), p. 86 and "Rhode Island Genealogical Register 3" (1980-81):239.
The Catherine Arnold that married James Ballou Jr., 25 Jan 1713, her parentage is unknown. Same Roberts source above, pg. 67.
Given Mr. Roberts expertise and association with NEHGS, I feel I should accept this for now, but I still want to review these sources at some point.