Right - the whole premise is that the government cannot compel speech (in the US). So if you publish something every week that says, “we’ve never been subpoenaed as of this week” and then receive a subpoena, the government can’t force you to lie and publish the same note afterwards. The lack of it being published is the canary here.
Whether you can be compelled to lie under these circumstances or not is not a resolved question of law. Although it seems fairly likely that compelling speech in this way is unconstitutional, if it has been tested in court, the proceedings are not public.
Good thing no one is doing anything unconstitutional right now?