If he turned himself into the police, does that mean he arrested himself as well? Was it the entire force or the station he turned into? Perhaps he turned into a cruiser or a canine officer. Oh, the unanswered questions.
One would think the brilliant journalist who wrote this article would realize turning oneself into something else entirely would be the much bigger story here. Focus writer, focus.
I don’t understand your point. The phrase has been used as a accepted way of saying a suspect surrendered to the police for decades.