It's a management role. They want you to understand and navigate the bureaucracy involved in being a middle manager in city government. Negotiating with Czar of Trash in order to make that real solution a reality, is probably more important than being an expert trap maker. But you definitely want that person on your team!
The nature of the description makes more sense, given that. It sounded mis-targeted at first, but I was assuming they wanted someone who would actually be waist deep in filth and killing. They want someone to put a hip and sanitized face to those people, but who is also unconventional enough to respect them. They put a line in a about being hands on, but presumably that's a photo-op type/learning thing.