I'm unable to see the link you mention, so my apologies if I rehash it in my comments.
"Does military culture matter?" Yes!
Simply look to how the culture of Japan's army twisted the entire country's foreign policy for more than a decade. The Japanese system of government of the time required that an active duty member of the army and navy be included in the government. All either service needed was to withhold a member from the government and it would fall, giving the services effective veto power over the government. Read over the history of how the services were unable/unwilling to reign in even the most extreme actions taken by relatively junior officers: government by assassination, officers on the mainland of Asia starting the war against China not only without orders from the civilian government, but even without approval of the heads of the army on Japan itself, and even direct physical assaults by junior officers on their direct superiors. The Army's culture of death before surrender was so pronounced that it not only led to island garrisons suffering death rates of nearly 100% and the kamikazis, but also held fast for the nation as a whole. Arming civilian women and children with pikes to resist a modern enemy shows the extreme situations that such a culture can create.
Look to the losses in Europe due to WW1 and the lost generation of men from some countries' populations. The UK, Germany, and France (at least) lost so many men of reproductive age that they were still feeling the effects decades later. Imagine how history would have changed had the late war mutinies in the French army either never happened or had happened a year or more earlier.
While military culture never pulled a literal trigger, it's important effects on those who do cannot be denied. Contrast the quote from Patton to the Japanese mindset in WW2: "Your job is not to die for your country, but to make sure the other s.o.b. does." The Americans were not submerged in a culture that told them to win or die. In such a system, with death as the alternative, anything becomes acceptable.
Contrast the fate of occupied peoples under US control in WW2 to those under German or Japanese control. Despite the racism leading to the disgraceful treatment and imprisonment of Japanese-Americans, the record of the US as occupiers was relatively good. The Rape of Nanking, the Battan (sp?) Death March, the Holocaust, and others speak for themselves. The military culture of each nation made such events possible.