I don't know about police departments, but every big company I've ever worked at outsourced their shredding. Any sensitive documents went in the shred bin, which was periodically picked up by the shredding company. It makes no sense to me either.
Everywhere I've worked, the bin has always been "secured" with a three-pin lock that can be picked with a paperclip. That's a good way of expressing how seriously document destruction is taken.