Hi,
My guess would be that landuse=military was used for the border zone simply because there wasn’t any better way of tagging it at the time of its creation. That proposal would probably be a better way of tagging the border zone at least in my opinion. And yes you’re right, you can and need to get a permit in order to enter the border zone legally. So access=private is wrong, which again was probably probably due to access=permit being quite rare