Ending explained for those confused.

The couple said the childs name during the torturing. Why did he write the note? Because the mental influence of the torture actually broke his mind and convinced him that he was the killer. He didn't do it to "give the couple relief or closure". This made me think of an episode of Star Trek: TNG where Picard was being tortured. I may get the number of light wrong, so please forgive. The torturer told Picard that he would stop the torture if Picard told him how many lights there were. Picard would say Four, and there WAS only four, yet the torturer told him there was five and would torture him, trying to break Picard into saying he saw five, when there was only four. As a final act of rebellion, picard told the torturer that there was four lights. Later in the episode, Picard admitted that because of the torture, he actually eventually SAW FIVE lights. This is sorta similar. The man in the movie was tortured so much and told "you killed our son" that he was broken down and convinced by the torture that he REALLY WAS the murderer. Naturally, he felt guilt and killed himself. Yes, they had the wrong man. But, due to the torture that broke his mind, he was convinced that he really did it. My apologies for any misspellings or gramatical errors, it is very late.