Physical fitness is, IMHO, paramount in ANY survival situation. You are looking at a stressful situation; being physically fit, your body is more prepared to handle that. You certainly have a higher chance of survival, all things being equal, than someone who is out of shape. Yes, mindset also plays a huge factor into this-but, take that out of it, when you are dealing strictly with physical/physiological ability, the person in better shape stands a better chance.
Now, I think, personally, there is a plateau-having 3% body fat isnt likely going to help you in certain situations. But, I think having an average fitness-someone who jogs regularly, or walks, does some weight training ie a general overall decent fitness level-has a better chance than someone who doesnt do anything at all.
Now, speaking from personal experience; I served 12 years as an infantryman in the US Army. Not a necessarily easy life. We were physically active every single day-runs, ruck marches, HMMWV pulls-the idea of course being that you develop a high level of fitness, and maintain it. Now, since I got out, of course I slacked off . But, all of that training had taught me that, if I think I can do it, I just suck it up & do it. If I DONT think I can do it, think again! As we used to say: sometimes, you just have to embrace the suck. Could I run 8 miles now? Probably not. Could I jog/walk it? Yes. Physical fitness isnt where it was, but the mental toughness is still there-and that counts for a lot.

As to what military standards are for physical fitness; there are the BASIC standards, which all US forces must meet. Then, at least in the Army, there was what was called "Fit to Fight". You have to achieve at least 70% of all categories (my understanding is that there are different tests now-it used to be situps, pushups, and a 2 mile run). In almost all units I served in, you had to achieve a MINIMUM of %80 every 3 months. We tested every 12 weeks, if we werent in the field. If you failed to meet the 80% criteria in ANY of the categories, you had double PT-one in the morning, one in the evening, until the next test. Alternatively, if you score 100% in all 3, you didnt have to do PT at all-they figure whatever you are doing in your offtime is working