Eveofchaos
I was thinking. Khan walks around with the "cell phone" provided by the Global Army. This device was supposed to monitor soldiers. Record their location, record what they say, record their surroundings, even their health. These are pretty simple things to do that even a regular cell phone would do. Even with no connection it is possible to simply record locally on the device. So Khan betraying the Global Army and having a relationship with an alien is no secret. If they don't know, then the Global Army is stupid for not monitoring these devices. Or it could be a hole in the script as well. It makes no sense for an army with such advanced technology not to pay attention to espionage.