The private nature of the company is the specific thing that matters here. It is right to emphasize that through use of the adjective. You’d better ask “why use the word ‘company’ at all” and the answer is that it’s a useful noun upon which to supply the critical adjective.
well, in the US, the First Amendment would start come into play in interesting ways, depending on whether the content itself is considered an expression of the government itself or just general.
