Then people should stop stating the former as an argument, because "all speech should be free from all consequences" is what it means.
Similarly, people say that some countries have freedom of speech, when in reality every country has ways of punishing people for making certain noises out of their mouths - they just differ in which noises and to what degree.
The effect of this dishonesty is there is a hidden social contract on what you are, or are not, allowed to say, and everyone has to negotiate that. The article is about how people are becoming more self-censorious as a consequence of this social contract tightening up.
That phrase is always proposed as a rebuttal to "freedom of speech doesn't mean freedom from consequences," and always in the context that any consequences given will lead to a slippery slope. It doesn't contradict that premise at all if interpreted in the weak form, it only makes sense as a rebuttal in the strong form.
So either the so-called "free speech maximalist" side actually believes that people who argue free speech doesn't mean freedom from consequences are referring to all consequences rather than any consequences, or else we're all just in violent agreement with one another, and really just haggling over what those consequences should be.