I often look at verses like those through the viewpoint of the book of Job. In the book of Job, Job's torment isn't divinely appointed or prescribed by God; rather, God seems to withdraw from protecting Job, and Satan is allowed to have his way within certain parameters. Job's questioning of God's justice throughout the book seem to culminate not with God's response of "Well, Satan asked for permission, so I granted it to him." Instead, God seems to respond with "You are just a man. What do you know about the way I work?" We all know in chapters 1-3 that Satan caused the calamities, but God didn't place the blame on Satan when questioned about it.
In Saul's case, I would say the same. God withdrew, the evil spirit did its damage, and God -- not responsible for the evil spirit's work -- didn't place the blame. Or at least the writer/ recorded didn't place the blame.
In any case, we have to steer away from explaining away the evil spirit as a psychological disorder.