Google will probably do a better job in every way, including security, than the city of L.A. I'm sure leaks from city employees or people stealing physical paper will far outweigh any IT related leak.
The funniest thing about this article is it is supposed to scare you that L.A. is switching to google services, but the article mentions Washington D.C. is already doing it.
As someone who worked for the city of Los Angeles I doubt the security part of your claim is true. People assume the government system is so backwards that it must be inferior in every way but that backwards-ness actually makes it more secure because a lot of their documents aren't on a publicly available intranet. Their system is so antiquated that most transmissions are done via modems which, if you think about it, is more secure.
I'm not suggesting LA stay backwards for the sake of security. But once they jump into the world of putting docs on servers that can be accessed by the public there's going to be a lot of new risk involved. Google's security track record isn't exactly great (http://broadcast.oreilly.com/2009/05/google-failings-say-lit...) which makes me question the wisdom of trusting them simply because they're the cheapest option.
Put it this way. Next time you're bidding on a contract against a guy who will do anything to win how secure will you feel knowing all your private records (medical, divorce, business) are housed on Google Docs?
The funniest thing about this article is it is supposed to scare you that L.A. is switching to google services, but the article mentions Washington D.C. is already doing it.