It seems to me it's just a matter of definition. Clearly it was a conscious decision, since they are able to talk about it. They even say they were "just about to push the button". The only confusion is that they also claim they hadn't "decided" to do so. So clearly there is no issue with the "conscious" part, but perhaps some confusion about what constitutes a "decision"?
I mean, what does it mean to be "about to push", if not that they had infact decided to?
Our brains are already known to lie to themselves to make things appear synchronous that aren't actually synchronous. For example, syncing sound in a TV broadcast makes use of this. And I believe it's the same story with limb motion and tactile feedback. If you touch your finger, then it seems to feel like you touched it immediately despite this feeling requiring some time to work its way to your brain.
One interpretation of the experiment is that your unconscious brain decides to push the button and then tells your conscious brain to make up a story about how it was the one who made the decision.
Another interpretation of the experiment is that your conscious brain decides to push the button, but then your unconscious brain messes with your conscious brain's perception of time such that you'll believe that the button press is happening simultaneously to when you make the decision. The end result being that you "feel" like the slide changes happens before you decide to do it.
All "conscious" decisions necessarily have to be made by unconscious processes in the brain, because consciousness itself is a result of unconscious processes. Every conscious decision is thus made by unconscious processes. How could it be any other way?
However, people mistakenly take this experiment to mean that we don't actually have conscious control of our actions. That's incorrect. Think of conscious decision making like a two step algorithm, "conscious" decision making by unconscious processes + store decision in short-term memory = conscious awareness (this is one possible model, not necessarily the model). If the system in the experiment can read the output of the decision making step faster than it gets stored in our memory, then it will produce the results described.
This is incorrect. Libertarian Free Will, the type you seem to think humans have is an illusion and does not mesh with reality. No serious Neuroscientists or Philosophers of Mind believe it exists.
Note: this has nothing to with the political bent of Libertarianism.
Lots of free-will-stans here mad at reality.
However, this also isn't just taking out the middle step. If it were, the advance of the slider would feel like it happened instantaneously as soon as we are aware of making the choice consciously. This is showing that our conscious awareness of making a choice lags the choice actually being made at a level we are not conscious of.
I don't get it. The effect (the advancing of the slide) doesn't precede the cause (you deciding to advance it). The thing here is only that they dispensed with the middle step of physically pushing the button.