When I went through boot camp (20 years ago mind you) there was plenty of CW going on and their food was still high in fat. It was also high in carbs, but there was nothing lean about it. LOL.
If I were you, I wouldn't worry too much about being Primal while in boot camp. You will be working/running your ass off and will need ALL of the energy from food that you can get. I am not saying to eat the donuts in the morning (you won't get those for weeks anyway) but you can eat pretty much everything there and you will NOT get fat. Don't tell them you are a vegetarian. You don't want to stand out for any reason. Trust me. My Dad was a Colonel when I went through and they found out (I have no idea how, I never spoke of it) and they made my life a living fucking hell for 10 weeks because of it. I got all sorts of extra duties, double fireguard AND I always had to add on 6 of whatever exercise we did (Colonel is O-6).
I can't imagine the horrors that would befall you if you told them you were different than everyone else. That is the last fucking thing you want to be in boot camp, different.
In the mornings, stay away from the juice and go for the milk. Eat eggs, shit on a shingle (chipped beef on toast), or even oatmeal (if that's the best option).
Lunch and dinner usually consists of some sort of meat substance (boiled, always boiled), vegetables/salad and a carb source like potatoes or rice, which you will need to eat. Just stay away from the breads if you can and you will do very well.
With the amount of physically demanding work you will be doing, you actually do want to spike your insulin to get the nutrients/protein into your cells. I know that is counter to what I said in PrimalTatooLovers thread, but he isn't in boot camp. You will get much stronger and your endurance won't suffer.
People too weak to follow their own dreams will always try to discourage others.