I just did a bit of insomnia-induced reading about this, because considering my luck with being smacked with biking citations I wanted to know whether I was required to register my bikes that are in LA. Fortunately, I'm not, and neither was Aguilar. According to the LA Times,
Long Beach eliminated the law mandating bike registration five years ago. Bike Long Beach should update that page. It does clarify on another page on their site that they do not require bike registration but recommend it so the bike is identified as yours.
I'm 94% certain apartment buildings do not qualify as a business area in Long Beach or elsewhere in LA, because if they did a huge swath of the city as well as the county would be classified as such. Some buildings are mixed residential and retail, but the majority are not. Long Beach prides itself on being the "most bike friendly city in America," and if you couldn't bike in any area with apartment buildings without fear of a citation it would make it one of the most intolerant cities of bikers. Besides the tonier gated communities I don't know of too many areas there where there aren't apartment buildings.
Los Angeles is the name of both the massive county and the highly populated city. Long Beach is a city within Los Angeles County. You do not have to register your bike in Los Angeles, the city, or in Long Beach. Once upon a time you had to register them in Santa Monica and Beverly Hills, but it's not mandatory in either city anymore; both cities do provide optional bike registration for residents. Some cities in LA County might require bike registration, but I'm not aware of them. Each city has its own ordinances, and its own discretion in how they are enforced. I discovered that the aggravating way when I was given a $197 citation for being a minor not wearing a bike helmet on a day of record-breaking beastly heat and Santa Ana winds that felt like a hundred hot blow dryers pointed at you. Most people weren't wearing helmets for mellow leisure rides that day. A police lady just stopped me randomly and cited me. I went to the police station the next day to ask them about it, and the officers were visibly flabbergasted. This one kept saying "that can't be right." And then he went and found out that in fact, it was right for that city. If I'd been an eight of a mile away over the city borders I'd have just been given a reminder to wear my helmet next time because that's their policy.
At my college we do have to register our bikes and will get cited if we don't. You just get a sticker with the registration number and expiration date that you put on your bike. It only cost $3.50 and is valid for three years. It would be kind of adorable to have tiny bike plates, though.
Anyhoooo. I need to get some zzzzzs. I doubt the actual reason for the stop was related to any bike-related offense.