I think, assume. With the Military, with the goal of killing people, that there is assumption of more human judgment being involved. Beyond even the issue of a man-in-the-loop for targeting systems. But even generally, that these are big decisions that shouldn't be farmed out completely.
For every job in the private sector, there's probably someone in the DoD doing the same thing. In 2005, the tooth-to-tail ratio (combat to non-combat roles) was 1:8.1.
I'm guessing the vast majority of the AI usage is for things any typical office worker would use it for.
I presume they might view their internal data being used to train a private company's training sets as a concern.