I will have to find an excerpt or transcript of the documentary to know what it really said about physics.
But deducing anything about the mind or about people from physics is full of problems. Free will is just a small part of it. Physics as we know it basically doesn't contain people or their experiences; just lots of atoms bouncing around. There is no self, no conscious experience, no color... just atoms arranged as bodies. The human race has invented dozens of crank doctrines trying to explain this away. Most of them are a sort of dualism, e.g. the brain is physically just an arrangement of particles, but then it also "has a feeling in it" and that's you and your experience of being alive and in charge of your body.
So on the free will question, the most popular position is "compatibilism" and it says that your decision-making is somehow the same thing as the physical cause-and-effect, whereby what happens in your brain determines the actions of your body. And that sounds somewhat plausible, but it still has this dual interpretation going on, which I think is the real problem.
Also, another complication is that quantum physics isn't deterministic, it just deals in probabilities. Sometimes people use this as a loophole for free will, but the whole point of free will is that you and only you determine your actions, not that your actions are determined by the random behavior of subatomic particles.
The randomness of quantum physics raises its own issues which have nothing to do with free will. Such as, isn't it strange for something to just have no cause at all? If they don't have causes, how do they still "know" how to behave so that 50% of the time they do one thing, 50% of the time the other thing? And basically it seems to run against the whole idea of a predetermined future - but again, I'd have to see what Brian Greene actually said.