Hence the reason why I call it a pet theory. That being said, there are potential mechanisms. Take, for example, shot noise at low light levels. The sensitivity of the human eye is ~5-9 photons within a 100ms period - well, actually, down to a single photon, before filtering[1], but 5-9 before a signal is sent. That is well within the realm of shot noise being significant. Or, for another mechanism, we know that triggering individual neurons can have specific macro-scale effects[2]. Although I haven't found anything on the minimal random fluctuations to trigger a neuron (15mV? But I do not know the capacitance, and as such that value is meaningless to me), and I suspect it is far above the scale at which quantum effects are significant, we do suspect[3] that neurons employ temporal encoding, and we know that neurons fire relatively often (often 10-100 Hz). As such, "edge" effects, where a neuron is or isn't pushed over the edge into firing are a potential mechanism.
But as for the rest of it - "in the materialist view, you cannot have any free will or any kind of ability to make a non-determined choice". This is what I disagree with. Non-determinism arises through (for example) shot noise, and as for free will... The effects of randomness on a system and the effects of "free will" on a system are equivalent. There is no way to tell if a particular decision was randomly decided or if it was the result of a decision by a sentience. Entropy of a signal is at its maximum either when something is random noise or if it is perfectly compressed data - and perfectly compressed data is indistinguishable from noise.
[1] http://math.ucr.edu/home/baez/physics/Quantum/see_a_photon.h...
[2] http://www.extremetech.com/extreme/123485-mit-discovers-the-...
[3] https://en.wikipedia.org/wiki/Neural_coding#Temporal_coding