Consider your human brain, and the full physical state, all the protons and neutrons some housed together in the same nucleus, some separate, together with all the electrons. Physics assigns probabilities to future states. Suppose you were in the middle of a conversation and about to express a next syllable (or token). That choice will depend on other choices ("what should I add next"), and further choices ("what is the best choice of words to express the thing I chose to express next etc. The probabilities are in principle calculable given a sufficiently detailed state. You are correct that LLM's correspond to a probability distribution (given you immediately corrected to say that this table is implicit and parametrized by a geometric token relationships.). But so does every expressor of language, humans included.

The presence or absence of understanding can't be proven by mere association of with a "probability table", especially if such probability table is exactly expected from the perspective of physics, and if the models have continuously gained better and better performance by training them directly on human expressions!