Oh come on. I don't know enough to have a real opinion on the overall situation, but surely you can see the difference between "no cost to the federal government" and "no up-front monetary cost to the federal government".
Yes, instead of revenue going to the government, it's going to Booz. Just because it doesn't go through the government first doesn't mean it's not a cost. This is proven because Booz wouldn't make and run this site if not for this aspect of the relationship.