Of course factors other than genetics determine the state of the neural network, but the way in which it effects it is in turn determined by genetics. Why more than one to change my mind? Because there is plenty we don't know, and a myriad of potential explanations. I'm just surmising that we are biological automotons transitioning from state-so-state based on the culmination of inputs into the perpetually changing neutral network structure established by our genetics and shaped by the environments impact on it, which can also largely be determined by the same genetic code.
Environment and genetics are inseparable, of course, so it's "impossible" to test. I can't prove it, I'm just asserting my theory based on the known evidence. I don't "know", but I still believe my theory is correct. That's the distinction. I acknowledge I don't know, and likely never will. Same as you, right?
You've seen the same evidence, and come to a different conclusion. That's fine, but you can't prove that human intelligence is non-deterministic any more than I can prove that it is. So we'll just have to agree to disagree. I hope that you are feeling gregarious enough to concede that.