My view is that this is primarily dominance hierarchy, with a smattering of more organic tribalism in there. In Sapiens, I'm reading about how once you get past a group of about 150, cohesiveness and trust cannot be maintained through personal knowledge, and so it must take place through shared myths, beliefs, stories, etc. This goes beyond the most surface-level meanings of those words to include what is essentially the ethos of the group. One great example, that I want to write about more at some point, is how there is a worldwide belief in money, even though it is largely just a symbol (a piece of paper or a virtual transaction). And yet, all around the world, people are bought into the "story" of money. If an organization is bought into the story of violent domination as the way to succeed, garner respect, keep order, etc., then that's what is going to be the ethos of that organization.
I agree to some extent that top-down isn't always enough, but in a very hierarchical institution, those nearer the base of the pyramid do take a lot of cues from those at the top. That's why top brass got canned at Fort Hood - they allowed for and turned a blind eye to a toxic culture, refusing to call offenders into accountability, and people died. That's what the sec of the army meant when he said that leadership is vital because systems alone are not enough.
As I've often said before, the culture of any society or institution is the one that is tolerated. In a swinger's club, disrespect of women is not tolerated, and so it mostly doesn't take place. We're a culture that glorifies violence (see every action movie ever as evidence of this), so until we begin to change that story, that there are other ways to be tough and strong other than "might makes right" we're going to keep getting the culture that we have, both inside and outside of the military.
Edit: The community of Catalhuyuk, which had 10,000 people at its peak, went for thousands of years with no leaders and a highly egalitarian social structure. The anthropologist who heads that site now attributes it to a series of beliefs and norms that kept the group cohesive, despite no leadership structure. So, imagine what stories and norms that don't support the violent domination of others in your society might do when they are supported by leadership. The problem is, in a dominance hierarchy, only one person or group can win, and if you don't win, you lose. One is always one-up and the other one-down. This is why you have deployed vs. stateside, and grunts vs. POG, and men vs. women, etc. Any natural tribalism is reinforced by this divide that says it can't be win-win, only win-lose and you want to be darned sure you are on the side that wins.