I found this newspaper article about the incident:
Aug 26, 1862 – NY Tribune
Letter from captured soldier at Camp Texas
“I have seen to-day a terrible sight on this side of White River, four deserters executed by order of Gen. Hindman. Deserters are leaving us constantly, going in companies of eight or ten in the same way. The Company that I am in and Blackburn’s and Hooper’s men, are put together. I will stay as long as they feed me, and that is all I ask of them. There is a great deal of dissatisfaction in this brigade. There was 110 left Morgan’s Battalion last night. They take their arms with them. They are doing so all the time. They will all be shot. There is no other way to put a stop to it, but to put them to death.”
Whoever wrote the piece for the NY Tribune said they would not name the soldier who wrote the letter because it was assumed the letter writer was in the army against his will (conscripted) and didn't want to be there, and the columnist didn't want to cause him harm.