That I don't disagree with. It depends on what one considers "free will". I think that without an agreed upon definition of what these words (free will, determined) mean, it's not very useful to say one or the other is or is not involved.
I think the original article is suggesting that "free will" is the same as conscious awareness of some decision. By that self-declared definition, then of course they are right that there is no free will involved, because they've defined "free will" as conscious awareness of the decision. Since unconsciousness is not consciousness, then by their definition it can't be free will.
I don't have the same definition, so I don't agree with the way they phrase their conclusion.