That's a huge oversimplification of the way LLMs work. They're not statistical in the way a Markov chain is. They use neural networks, which are a decent analogy for the human brain. The way the synapses between neurons are wired is obviously different, and the way the neurons are triggered and the types of signals they can send to other neurons is obviously different. But overall, similar capabilities can in theory be achieved with either method. If you're going to call neural networks statistics based, you might as well call the human brain statistics based as well.