The NSA* or any other similar actor can load malware to your phone that would prevent it from being completely turned off, the police most likely cannot.
The police does have a vested interest in making the public think that turning the phone off is pointless.
*on older phones like late 90's very early 2000's there was enough power leaking from from the antenna into the modem part that you could ping turned off phones remotely even if the battery was removed I've seen this in action. This doesn't or shouldn't work on new phones which require considerably more power and have very complicated hardware.