Well, technically there is a difference between a "company" and a "corporation." A company can be privately owned. A corporation on the other hand, is not privately owned. A corporation is owned by the shareholders, thus not private.
Here's an example: There was a case a good many years ago in which a lawsuit was brought against a privately owned club for not allowing women. The plaintiffs lost because it was "privately owned" and as such wasn't open to the general public, so it had the right to say who could or could not come in. Over time, that club did change its policy, but it had nothing to do with the case they defended.
In the case of the Tech giants, they are corporations and thus, owned by those who purchased shares in their stocks, thus not private. Just because you own shares in a corporation's stocks, doesn't mean you are in agreement with that corporations policies. If you own enough shares in a corporation's stocks, you do hold sway on corporate policies (just being the major shareholder doesn't ensure that yours is the only opinion that matters). If enough individuals who own shares band together and protest, the major shareholder (generally the CEO, rather than the president) can be voted off the Board of Directors.
The lawsuit against the Tech giants may go nowhere, but some of that is how many in the lawsuit may be shareholders that believe in free speech and don't like what their own corporation s doing.