I think that your first example is also not a violation, as it is not an opinion. I think that this example reveals a more potent problem: what do we classify as opinion? As to that, I have no answer; I am no philosopher.
As for the morality of restricting others' right to free speech, it is definitely a difficult problem. Morally I think that you have no right to silence others because you disagree with their opinion. There is some nuance here; if HN deletes a post advertising viagra I don't think this is silencing someone. Similarly, deleting a post containing the results of a football game to a programming forum is also not silencing someone. There is an aspect of relevancy at play. If you choose to operate a general purpose forum, morally you are pretty limited in what it is acceptable to silence.
These are just my off-the-cuff thoughts. I might be missing something obvious here; it seems like a confounding problem.