General Stone is not a moron. He acted fast, without remorse and emotion. He did what had to be done. The only moron are those who helped to take infected children over the border.
...as for the reason Doyle was killed, it was a possible threat and a risk. No exceptions, he had to be put down.
I thought they did that because of the way he was moving towards the car. Like the other infecteds, he might have looked to them like he was desperately trying to reach uninfected people inside the car. Or just acting frantically.
Besides, they had already had an order to kill basically anything that moved. And/or, the fog could have been a reason why they didn't recognise him as one of theirs in the first place. They saw something moving, they weren't in a place to take any risks. They just had to kill him.
Once Doyle abandoned his post on the rooftop, he was fair game. Everyone at ground level was to be eliminated with extreme prejudice.. It didn't matter anymore who was a soldier and who was a civilian.. The only folks who were safe were the ones dispatched in the ground team with the flamethrowers..They were still doing their job, and were meant to be there. People don't get that's how this works IRL.. With a highly contagious outbreak there's 1. Containment 2. If containment fails, you attempt to regain control and kill the infection..if this doesn't happen then 3. Completely eliminate all trace of the virus & its possible carriers..
In this case, the gas took down the infected (and anyone else left alive) not killed in the firebombing of district one, and then the ground troops followed behind to burn the bodies to stop any possible spread of infection.