Thanks for your help - as soon as I sent the email, I noticed that the date was wrong. William Walker Fitts was a brother to my great-great grandfather who lived in Madison County [Danielsville, Georgia] - the 16th was assigned to the Army of Virginia but I have found out nothing there.

After having read the various accounts of the Battle of Spotsylvania Courthouse, it seems that the Confederates carried the day; however, it was quite a "bloody" battle with the living piled among the dead so you are probably correct about his interment.