While that's true (and I agree with your definition in the context, which is not political), the root of the misunderstanding is modern liberalism stealing the word from what is now known as classical liberalism
Even if I interpret it in a polical way, I would still take "more liberal" to mean "supports greater freedom of speech"; that's consistent with what you call classical liberalism. I hadn't heard of this "modern liberalism" until now, which seems to be an American term. But looking at the Wikipedia article [1] it doesn't seem to involve much discussion either way about freedom of speech, except to do with donations by corporations (it seems a stretch to connect that with willingness to legislate about libel). If anything, the other parts of that article still have a strong enough similarity to classical liberal principles that I would expect an American "modern" liberal to still be in favour of free speech.
