Pardon my comments from the "peanut gallery" as I'm from out of state and unfamiliar with your situation, or the bureaucratic process you seem to be going through, but one thing I am in HUGE support of is any line of questioning or inquiry that shines a spotlight on hypocrisy concerning my pet issues.
(One of my favorite things is to ask the most progressive, feminist, pro-choice liberals if they are in favor of a woman's right to choose whether or not to use a firearm to protect her own body, or if the government should make that decision for her.....then stand back and watch the gears in their heads begin to lock up.)
It sounds as if the 'gubmint in your area seems to think ownership of firearms needs to be disclosed "for public safety".....but when asked about their ownership of firearms, they refuse to disclose ownership "for public safety".
I would definitely ride the horse until it dies. But, that's just how I am and my 2 cent contribution. I would, at minimum, write letters and make inquiries to authority figures involved clarifying the dilemma of whether or not the disclosure of firearm ownership is a matter of public safety. If it is, I'd kick the horse until I got a satisfactory answer on why, if disclosure of gun ownership makes society safer, does the city refuse to participate in the disclosure they tout so highly.
(While you're at it, ask them if high capacity magazines have any legitimate value for self-defense. If they parrot the old "high cap mags are only good for killing large amounts of people as quickly as possible" crap, ask them if their SWAT team issues them. If so, ask them why they need to kill large numbers of people as quickly as possible. That's another one of my favorites.