You can't make that assumption. Note that Lorenzo Temples was sent to the hospital at Lauderdale Springs MS. Needham may have gone there as well.
When a soldier became too sick to travel with his regiment, he was turned over to the medical service. Communication being what it was, the regiment often lost contact with a sick soldier at that point. If Needham Temples died in a distant hospital and the surgeon in charge failed to get a note back to the regiment (or the letter was lost or destroyed in transit), how would the company clerk have known what became of the man?
If you have a map of Mississippi from that time, you'll note that the Mobile & Ohio Railroad ran right along the eastern state line to Corinth MS. Confederate hospitals and military posts could be found at towns all along that rail line. Sick and wounded soldiers were sent down the rail line from the army regularly. If the first hospital on the line was overcrowded, patients were sent to the next available facility.
For that reason, it's impossible to know where this man might have been sent, but it's a safe guess that he was sent somewhere along the rail line.