I don't think it's so much a conspiracy, just reality of what would happen. I'm sure the government would declare martial law in a situation like this. Shooting survivors down in the middle of the street? I don't know, but I could totally see that happening. I understand why they are removing the very sick. They don't want them dying in the safe zone and then spreading the virus.
I agree. So far we haven't seen anything that doesn't make sense.
Shooting the uninfected in the street? Imagine the scene: A bunch of 19 & 20 year old National Guard soldiers or reservists who have never seen combat, trying to deal with the dead rising up and eating the living. Civil unrest in pockets around the city, fueled by lack of information and misperception of some of the early incidents (like the viral video of the police shooting the "homeless" person) as well as the usual social tensions. A panicked uninfected, running away from walkers or towards soldiers who represent salvation, not obeying hastily shouted instructions. Yeah, I can see how that would result in some unintended casualties.
Remember, at this point they don't know how it spreads. They know it isn't just the bite, but they have no way of knowing that it isn't a conventional exposure-incubation-onset model. From that perspective, it make sense to detain or even eliminate those that are "exposed". When they took the neighbor's husband, it was because he had the blood of the infected all over him. For any known illness that would be a risk factor for spread, and at least at that point they seemed to be trying for containment.
Even removing the ill and unstable from the community makes sense. They do know that every dead person turns, and the soldiers are outnumbered both by the fearful living and the walking dead. They can't risk the panic that would ensue if someone turned in the midst of a safe zone. Even if the walker was put down easily, the effect of the public realizing that it will happen to all of them could destroy what safety they've established. And clearly they aren't just killing those people; they're taking them to that holding facility where presumably they're trying to learn more about the infection.
I think this week's episode did a lot to pull things together and start moving the story forward. I had a hard time getting into the first few episodes but as they've started showing more of what's going on outside of the neighborhood it is getting better.