well unofficially, at least so they say, in the very beginning, the lightweight fighter program was conceived in secret by 5 guys in a back room in a pentagon - John Boyd, Pierre Sprey of the Close Air Support/A-10 fame, and a couple others known as the "fighter mafia". Much of the specs, requirements, and various aerodynamic parameters were determined before the bureaucratic majors and colonels knew about the project. The prototype aircraft were designed by engineers as side projects at Lockheed and Northrup, more or less under the radar. It probably helped that all the bigwigs were haggling about the F-15 at the time, which acted as a smokescreen.

It wasn't until it became apparent that the YF-16 was the real deal and probably going to be successful that it was finally exposed to the Pentagon procurement process, where it started to put on the pounds, and lost a bit of the agility that made the prototype aircraft famous (i.e. it had delta kinetic energy moves that the F-22 and F-35 can only accomplish via thrust vectoring).

The LWF (lightweight fighter) project was a well publicized procurement program. The YF-16 wasn't designed in secret, it was part of a three way competition between Boeing, Northrup, and General Dynamics.

The fighter mafia had tremendous influence in the development of the F-16 (and F-18), but it definitely wasn't a skunkworks program developed in secret and only unveiled at a later date like the U-2/SR-71 etc.