It's more likely that the military would provide soldiers with phones using a special version of Android with less tracking than it is that they'd mandate Google stop snooping on everybody for national security reasons. They take advantage of the data Google collects, the fact that everyone is carrying a mobile wire (mic and camera) filled with radios collecting and broadcasting location info, and that for many people a single device they carry acts as a treasure trove of information on them, who they've been talking to, and what they've been doing.
