BB&N was and remains a private company, and isn't primarily a government contractor. It was a one-time government grant — and for much less than the full CapEx required to build the thing. DARPA essentially said "you want to build this? We'd sure like something like that to exist, so we'll give you some money to increase your chances/make it happen faster."

As it turns out, "throwing money at American-owned private companies who are being the [technological] change you [i.e. the state] wants to see in the world, to advance the technological edge America has over other countries" is a large part of DARPA's mandate. DARPA seeks to incubate a healthy private sector in nascent high-tech industries, so that it can later rely on competition in those industries, to produce a healthy, non-monopolistic set of viable military contract bidders for the military as a whole to choose from / set against one-another.