Many contractors NEED access to both the military side, as well as the consumer side, to do their jobs. Take logistics, for example.
Some programs use common components (resistors, transistors, capacitors, diodes, nuts, screws, belts, fuses, ad nauseum). How do you see what you need from the Military side, and then research on who can either supply, or make that product without hitting Google (Yahoo, Bing, Dogpile, et. al) and then contacting a company website, if you are tied to a private, secure network? A private, secure network is great for talking to each other; but you can't use it to talk to anyone off the network.
KVM switch I have one on my deck right now, hit a button and my monitor, keyboard and mouse are all connected to a different computor. One could be on the secure net and the other could be on the internet. One possible solution out of many possible solutions to the problem you offer.