Assuming I understand it, the reasoning you described is fallacious regardless of anything having to do with human free will. True, the presence of something combustible is a necessary (but fortunately not sufficient!) condition for the occurrence of a fire. But if I were to infer from that fact alone that the presence of something combustible was the sole cause of the fire, my inference would be laughably bad: indeed, onlookers would probably construe it as a joke. In any case, it would be evidence that I don't really possess the concept of causation.
I think that a related but different fallacy is often committed by those who say that the physical necessitation of a human action always makes the action unfree. It's the fallacy of assuming that the physical necessitation of an agent's action always bypasses the agent's deliberations. If causal determinism is true, then my decision to respond to your question was physically necessitated by events that predated my birth. But that doesn't imply that my deliberations -- my deciding which questions in this week's batch to consider answering, my deciding which of those to go ahead and answer, etc. -- played no role in my eventually answering your question. (It's not as if someone else decided that I would respond to your question.) On the contrary, according to causal determinism, my deliberations were essential links in the causal chain that led to my decision to respond: there's no reason at all to think that I would have responded to your question even if I had never deliberated about whether to respond to it.
I hope my answer engages with your question enough to be helpful.