I think Thompson might just be having a little fun with his acting career.
The fact of the matter is, there were a good many Confederate soldiers that came to admire and respect Grant during and after the war. Then there were prominant confederates, like George Pickett, who counted Grant as a friend and James Peter Longstreet who considered Grant as one of his closest personal friend's before and after the war.
Longstreet was married to either Julia Grant’s sister, or cousin.