We're reading the responses to that stack exchange question pretty differently if your last line is your takeaway...in my opinion it would be extremely unlikely for a court to rule against "Big Tech" in this case.
For example I make a post on HN. It follows the community guidelines and rules. The post is factually accurate as well. But it pisses the ATF off so they request that HN censor the post and any other future post that may be made about the topic. HN news decides its better to not fight the ATF and censors the post SOLEY due to the governments request. In my eyes this type of situation is the government directly censoring a post they don't like. You remove the governments request from the equation and the post would not be censored as its follows the site rules.
As I can't find any existing ruling that deals with the situation above, I said that we won't know until the courts decide.
edit: spelling