The idea as well is that training can only compensate for innate survival practicality. There are some things that cannot be taught in a military training camp; logical reasoning under pressure, the ability to overcome fear (or at least function while under its effects), and so on. I'm reminded of that scene in the film 'The Road' (though I can't remember it from the book) where the bad stuff starts to happen and Viggo Mortensen's character satrts running a bath while everyone is going mental. He recognises immediately that water will be important. No military training, just a practical, logical thought process. People like that are the ones that will survive, not someone who knows how to fire a gun (in fact, given the types of people that typically own guns, it's likely they won't).
I would think that in reality people that survive wouldn't really be put into the military (or whatever passes for one). Firstly, everyone available has survived already, so what makes the protags special? Secondly, those in the military would likely have delusions of grandeur to the extent that they would see others as somehow beneath them. Anybody in a position of authority in that situation would hardly have greenhorns who haven't been brainwashed to take orders joining their team (unless of course they hated the newcomers, sent them on a suicide mission only to lose their power when our heroes return victorious and become idolised by the rabble).
I think if you're writing a zombie apocalypse scenario, you have to remember some basic things:
1. People like being told what to do (up to a point). It makes them feel safe, and that everything is under control.
2. In a world without consequences, people become animals. We all like to think we're evolved, but to be honest everyone is the same as they were when we lived in caves. We just have a fear of consequences that keeps us from taking whatever we want, whenever we want it.
3. The people that can provide food are the most important, and the people that can provide shelter are the second most important.
4. Just because someone can use a gun doesn't mean that they should be given one. Someone will inevitably use it as power over another.
5. Ruthless leadership won't last long, nor will a military one.
