Zombies cost money. This kind of reminds me of Sci-Fi TV shows where the aliens look like humans - (the remake of Battlestar Galactica) - it helps cut down the cost.
With that said, I can't imagine the govt saved all of Los Angeles behind 12 camps. That means they left millions of people outside the safe camp zones. So if there are zombies they are all heading to where the humans are easy to eat then when humans run out in the inner city they will head out.
Also, everyone still operates under the assumption that only the infected become zombies. When people die of ordinary everyday reasons this will confuse and cause panic in the camps.
With that said, maybe the govt higher ups already know everyone is infected and are moving out the sick so as to prevent them croaking and turning into zombies so that is why they rounded up heroin addict Nick as well as the other sick people and the mentally unbalanced. But they are not telling anyone below their ranks that all are infected.
Just a guess - I find the situation more interesting than what happens to any of the individuals the story is following.
I said much the same to my lovely wife during the show last night.
Walking Dead is an interesting character driven show, with zombies as the McGuffin.
Other Zombie movies are more of a "OMG! Zombies! Chase Chase Chase" -type trope, with some scares and blood thrown in.
I like "Fear" because we're presented with some horribly flawed characters. They've no idea what's going on (though we do) and they're trying to figure out ways to cope with it. Not much chasing. Not many zombies. I imagine we'll see more character development, but right now the show is more about the surroundings and events.