I do not disagree with you, I think the evidence clearly points to that area of New York, now or formerly known asDutchess Co., regardless of prior research reporting a Virginia origin.
However,the 1880 Census for Iowa has been around a long time, and as I pointed out John N Bates, son of Gilbert, stated on the Iowa Census that his father was "born in NY" and his mother in "Conn".
A quick look at Covey data, will show that Samuel Covey, the father of Rachel, was himself from Dutchess Co NY. And as I indicated, the 1835 Rev War Pension Rolls for Tenn show Samuel Covey as getting his pension based on service in the New York Militia.
Also, as I noted, the 1912 book "Historical and Genealogical Record, Dutchess and Putnam Co NY", documents Tax records in 1777 for an Isaac Bates and a John Bates, in addition to James Covey (likely James Hope Covey, father of Samuel).