Pure-Politicians aren't the ones who tend to end up as War Generals and those such advisors in the "war room", so to speak. While many do have political backgrounds, a great many of them have heavy historical background as well. They didn't become Generals by accident. They have sought to be in that position their most of their lives and have studied past wars and strategies extensively.

As evidence I will point to the numerous dozens of war-strategy/review books written by ex-generals and other people who used to be very high ranking in their (large) country's military. There are so many books just like this. While sure these aren't the guys who choose which wars to go to, these are the guys who are in charge of strategy and tactics during the war. They are the direct commander of the military. The president tells them what they want the military to do and assuming the general is compliant, he will formula strategy on how to go into the situation and achieve the presidents goal. That's the whole point of the position. In extreme cases of history, armies have been known to ignore their country's commander and in turn side with their general who they trust more (ie Military coups).