Free speech? What about the NDA?

It just hit me that all the countries that congratulate themselves on upholding freedom of speech and even try to shove it down other people's throats have a blatant breach of that principle right under their very eyes: the secrecy practices of corporations. When an employee is hired or fired, he signs a non-disclosure agreement concerning the activities of the company he joined. If he breaks that agreement, he is liable to legal pursuit, from the same legal system which holds freedom of speech as a sacred principle. Of course, it is understood that free speech should have exceptions. But the NDA is an institutionalized and universally agreed-upon device. Can corporations really be above the constitution? I smell a paradox here.