That's not the secret sauce, in the same sense that keeping source closed doesn't usually improve code quality from a security standpoint.
The other counter is there are 26 operators of the F-16. Frankly it would be easier both in practice and legality to get cooperation from some dude in Pakistan or Venezuela than a US citizen who can at least sorta be watched over.
Most of the tactics are not terribly advanced in the sense of some mysterious secret martial arts kick that defeats all. Most of the time battles are won logistically long before the fighting starts. Everyone in the business kinda knows what F16s do, not any more of a secret than knowing what Mig29s do, the struggle is always having enough resources in the right places at the right times to do anything about it.
Something that often surprises civilians is most US military manuals are freeware and have always been that way. If you want to learn how an Army Brigade Combat Team operates, you don't join the KGB and steal documents, you just download FM 3-96 and read it. This is why actual veterans get annoyed about fictional hollywood military stuff; if you don't understand the role of a BCT's information operations officer sufficient to portray one in a movie, its just sheer lazyness to make something up instead of simply reading the FM.
Its all part of the interesting strategy to handling massive public communications networks; half a century ago you could have an edge if it depended on having a secret sauce. Now that anyone with a web browser can download the official F-16 flight manual your strategy for having an edge relies on other forms of secret sauces.
A good analogy for the problem is that excellent world class scientific documentation exists for weight loss and athletic performance, yet most people will not train in those areas. Olympic athletes are not high performers because the textbooks for weight lifting are kept secret and only for their reading.