To me, this is in no way the case, so I assume I'm either failing to follow their argument or using a different definition of free will, but perhaps it's just a poor interpretation. Consider the following: suppose we hook somebody up to a device to measure their Bereitschaftspotential, such that they can see the readings. For full simplicity: say you're instructed to raise your finger whenever you "want to", and you're wired to a brain scanner such that you can see a light turn on whenever your Bereitschaftspotential is detected.
As far as I can tell, the people applying the experiment as evidence of lack of free will would argue that the monitor would light slightly before every time you raised your finger, and before you felt you had decided to do so. But if that's the case, then you would see the light before you "decide" to raise your finger. From here there are two possibilities -- to me the most likely is that you could then decide not to follow through with moving. This would mean that the monitor did not correctly "predict your action" -- it merely indicated that you were (subconsciously) focusing on or considering raising your finger -- getting bereit. You could use this to claim "impulses to act (or even 'ideas') rise spontaneously from the unconscious mind, without our volition", and I would largely agree. But whether or not we act on these impulses remains unpredictable to others but seems to us entirely within our control -- which to me would be if anything scientific validation of the plausibility of "free will", or at the least definitely not a rejection of it.
The other possibility is that you would see the light but not be able to change your mind "in time", which to me would indeed suggest problems with a notion of self-influencing willpower. But I imagine that the subjective experience of this setup would be indistinguishable from the experience "the light is forcing me to raise my finger", and while this outcome might well force me to reject willfulness, I have a hard time imagining that this outcome is possible. Has this test been carried out? Is it feasible? Unless I'm omitting some other possibility (say, you somehow perceive the light to activate concurrent to your 'deciding' to raise your finger even if another observer would see it preceding your time of decision), this experiment would quite readily either reject the "this says anything about free will" claim or give it serious credence.
I'm sure people have been thinking about this issue more in depth since the advent of the the experiment and the decades-old essays I've been reading. What is the current thinking on this matter?
Slightly tangential clarification: