Unfortunately, while the cell phone companies may have the right information to distinguish between official emergency service phones, they probably have no idea when personal cell phones are used for other official emergency operations. I'm in the utility industry - we have often used personal cell phones in areas where our radio system does not reach. Some of our electricians and linemen don't have company cell phones. I'm certain that doctors and other private entities are of the same nature.
Also, the towers that serve everyday users are often the same ones used for "official" cell phone traffic (not police radio traffic which is separate), unless the city maintains a completely separate cell phone system. The phone companies (Verizon, NexTel, etc.) cannot shut down a tower without shutting down all users near that tower. They can, however, shut down individual phone numbers or shut down all traffic except certain (presumably registered) numbers.
I'd venture to say that it would be much faster to have the police jam the cell phone frequencies as they can do this on site and don't have to contact all the various cell-phone entities. This would keep the effect very local. People a few blocks away probably had no problems with their phones.
That's because in a disaster, EVERYBODY in the area is going to try to call people at the same time, which would saturate the tower. This way, only emergency services phones work, and they have the whole tower capacity available