Unless the widow was with her husband at the time of his death she could not have known anything for certain. In almost evey case, a widow's pension application is based on heresay.
The best evidence we have comes from the soldier's military service file. The record for this man reports date and place of death as Dec. 9, 1862, Carroll County GA. There's no good reason to place either him or his regiment on Lookout Mountain TN in December of 1862,