You're making a good point, and I would suspect that it's valid in general.
I've definitely had unpopular opinions, and even when I don't, my questioning of the basis of a given argument is often misinterpreted as holding the opposite(and objectionable) belief. This isn't because I knowingly hold some dogma, but that I care about whether something is true or not. Even though I do think global warming is a real issue, I'm careful to point out whether or not a piece of evidence is specious because too often I've been classified as right wing or anti-science.
What I used to value about the internet was how I could have no-holds-barred debates with people from around the world and not be worried about my life being destroyed. From about the age of 11, I visited lots of anarchist and free-speech forums, sites about drug use, politics, etc., and ended up learning quite a bit having to argue with both total fools and those more savvy than I was. Even that young, what I valued was not the "criminal" aspect of these channels but the ability for myself and others to express their true selves, or at least the personae that people portrayed.
That's the internet I miss, but it's also the internet that took some skill to use and was far less profitable than it is today. Now that everyone is on it, the people want a level of safety that is dubious and stifles what originally made the web great. Joe Hacker inherently saw the value of libre speech, but the average person either doesn't understand that value or is afraid of being judged for holding that belief.
The internet isn't really different from anything else that we censor as a society. I don't believe that the same people who value freedom of speech on the internet would keep around entities like the FCC that quite obviously do not exist to protect the public from anything. The average person either doesn't understand what the FCC is for, or they would shrug and say that it's not such a bad thing.
I suspect that HN has a greater than average population of individuals who want an end to censorship online, but I would still agree with narrator in that most of us don't actually want a diversity of opinion. The reality is that most people are self-interested, and that usually doesn't mean that they're interested in hearing different opinions. They want the freedom to express their own opinions, but are still appalled when someone holds a radically different one. People are not very principled and they will move the goal posts out of convenience.
We may never see the old internet ever again.