It sounds like a truthful story to me. William David Bolt was my great-grandfather, and I heard several of his children tell how he would always cry when the song was sung, too. In fact, the kids would also tear up when telling the story. He was wounded in the arm and did not get all the way "from Atlanta to the Sea," but this was obviously a very important memory to the whole family. There seem to be Monts and Greens in every branch of the Bolt family and many others throughout that area, so the Mont who was on the March may have been W.D.'s younger brother or any of a number of cousins.
Was your grandfather's first name John? Was the store the one right at the intersection at Bolt's Fork, at the foot of the hill? From countless visits to family, I remember a second store, too. I recall the Fannin name at one of them, but not which one and don't remember John's last name.