This is a reformulation of two previous questions that seem to have been misunderstood, or most likely, I failed to make them clear. I thank all people that answered, even the belligerent ones.
Some terminology first: by classical I mean non-quantum, and I assume anybody trying to answer this questions do understand that difference. When we discuss if QM can be written in classical terms we mean a full description in terms of at least local hidden variables. Also by theory I mean what anybody means as a theory: some equations or computer algorithms written in paper, or anything equivalent to a formal system. I also assume we all know what is the difference between a theory (a simulation is also a special kind of theory) and the actual physical world.
For those unfamiliar with the violent discussions on this subject you can read this question, and this review article. Also a good popular science article with lots of references to the experimental results on oil droplets can be found here.
The question is pretty simple. The experiment on oil droplets show that what thought as a culprit of QM, the double slit interference experiment, could never be explained in classical terms. The oil droplets experiments showed that to be incorrect. Now the argument has moved to the statement that oil droplets will never be able to reproduce entanglement. Thus, entanglement is the new actual territory when we battle quantum vs. classical.
My question is not about oil droplets though. I take them as an example of a classical system that can reproduce behaviors that were previously thought to be exclusive of quantum systems.
My question is about another toy model, rule 110 cellular automata (CA). It is Turing universal thus it can simulate the behavior of any digital computer. The question is simple: digital computers can simulate entanglement and so can the 110 CA. Thus we have at least a toy model that has local rule hidden variables and reproduce entanglement.
Specific question: given this fact, what is wrong in claiming that entanglement could also be a classical phenomenon?