Factual error: This movie is set in 1935. Back then, executions were done by hanging. The Louisiana Legislature changed the method from hanging to electrocution in 1940.
Factual error: The cell keys carried by the guards do not date to 1935.
Factual error: When Paul returns home, his wife asks him what the doctor said. He replies "...gobbledygook mostly." The trouble is, the word "gobbledygook" wasn't coined until 1944. This scene takes place in 1935.
Answer: In addition to previous answers, it is probably also worth mentioning that they will never be able to prove it. Percy mentions multiple times that he "didn't know the sponge should be wet," even when they are back in the Green Mile and only Paul and the other guards are around, indicating that that will be his defence when they ever make it into a thing, knowing that they will never be able to prove otherwise.