What does "free will" mean? I think technically inclined people like us are easily led down the path you describe, but over the years I've become convinced that the kind of definition that leads you to "free will = random choice" is pretty pointless because it's so vacuous.
I like to take a step back and ask: why are we interested in free will in the first place?
In practice, what tends to be really relevant are questions like: are criminals responsible for their actions?
Free will is better defined as a shorthand for these kinds of questions. And in that context, it seems clear to me that even if our actions are purely deterministic, we can still have free will. What matters isn't whether our will is free of physics or determinism; what matters is whether or to what extent our will is free from the influence of other people and society.
Once you look at it this way it's also clear that there are no absolutes. We all influence each other, which puts limits on our free will, but we aren't just puppets, either.