Murphy in the context of the Execution ending is a cold-blooded killer who drowned his own son just so his wife couldn't have custody and killed a corrections officer who was never anything but good to him. It's likely he's a psychopath. Psychopaths, from what little I know of them, are very self-centered people who can go to great lengths to justify themselves to others, through lies and manipulation. With that in mind, here's my WMG, copied and pasted.
Going by the "Execution" ending, the game is how Murphy views himself, and/or how he wants others to view him.
As more or less, a helpless victim who's been through a lot of undeserved shit and fought back. "I never killed anyone who didn't deserve it," he tells JP. Charlie's murder, motivated by spite? That was the work of some boogeyman or an evil pedophile, certainly not Murphy himself. How dare one even suggest he killed his son, he tells the kid in the orphanage. Besides, just look at what Charlie's death did to him. Murphy ended up all alone in prison, having to deal with mean inmates and a bitchy ex-wife. Coleridge's death was all Sewell's fault, all his idea. He was framed! Don't you feel sorry for him?
In the context of this ending, Anne is the only one to see Murphy's true nature. Everything he says she believes to be a lie, a Wounded Gazelle Gambit, a set-up for a The Farmer And The Viper scenario.