A lot of companies will do that. For instance, I never identify on social media (including here) which company I work for. I am not authorized to speak on behalf of the company. Even giving it praise on social media is a form of communication, and I am not PR. Therefore, not authorized (of course, retweeting official communications or linking to them is fine). We may not like these policies (and it is kinda dystopian if you think about it), but once we identify as employees, we are representing the company.
Should I then decide to criticize the company publicly, I would expect the hammer to fall down, hard Not sure about termination, but it is always a possibility. Especially in the US, with at will employment.
You can blow the whistle. But that doesn't make one immune to consequences. Should it be like that? I don't know, but the matter of the fact is that it is like that today, across most corporations. Google is (Was?) somewhat of an exception, but even then most of it was on internal forums.