Since my preceding message, I have had the opportunity to research the vital records of Westerly, Charlestown, Hopkinton, & Richmond, RI. As I suspected, Francis the immigrant was a very early settler of Westerly, RI (he was there by 1693), which at that time included the other towns I just cited. And yes, the vital records are clear that it was Francis' son Francis, "JR", who married Hannah Bailey...
So "the book" is indeed very wrong for the first couple generations. RI Colegroves are from the southwestern RI Sabbatarian sect, which was founded in Newport but soon found its base in that part of the town of Westerly that became the village of Ashaway in what is today the town of Hopkinton. The immigrant Francis and his wife Hannah settled in what was then known as Shannock, just north of the modern day village of Shannock in what is today the town of Richmond, not far from Ashaway.
The "book" claims that the immigrant Francis lived to a promnent old age with two families in place unknown -- that is BS.
Interestingly, the vital records show that the immigrant & wife were illiterate, signing with their marks.