It's just a mildly grumpy trope. You don't really need to cross-examine and wikipedia-link every slightly venty turn of phrase.
In my country for example we had dictatorship until 1974 and there was censorship, done by a department called... Censorship.
It wasn't some kind of gotcha, it just seemed completely wrong and I'd like to update my assumption in case it was wrong.
You could also simply look at current events to understand the turn of phrase: Elon Musk, proud "free speech absolutist" bans Twitter accounts which criticize him, bans posts with the word "cisgender", and has manipulated the algorithm to prioritize his own posts.
It's a generic rhetorical flourish, those often come with a bit of hyperbole, aren't universally applicable, etc. That's a normal thing that happens when people have normal conversations, especially if they're a little worked up. It's this cliché, without the iambic pentameter
https://en.wikipedia.org/wiki/The_lady_doth_protest_too_much...
If you find something someone's said unclear, you're better off just asking instead of smacking them with a wikipedia link and then calling them a liar, though.
https://pen.org/report/americas-censored-classrooms/ this is from a few years ago but the trend continues