Yes, that James is the one in question. He was married to Ann Garner (1734-1810, d. of John Garner and Mary Rathbun/Rathbone), said to have died in Greenbrier. The person who attributed James's burial to Ohio also placed Ann there. Jackson history and family history document other sons and more generations, and many of those people are, indeed, buried in Jackson.
I've also asked about the records on this board's Jackson section. If James really is buried in Ohio, I'd love to see if there's any sort of account of moving his remains from Monroe, or Ann's from Greenbrier. Till then, I remain doubtful.
Thanks!