i agree, not just the multinomial sampling that causes hallucinations. If that were the case, setting temp to 0 and just argmax over the logits would "solve" hallucinations. while round-off error causes some stochasticity it's unlikely to be the the primary cause, rather it's lossy compression over the layers that causes it.
first compression: You create embeddings that need to differentiate N tokens, JL lemma gives us a bound that modern architectures are well above that. At face value, the embeddings could encode the tokens and provide deterministic discrepancy. But words aren't monolithic , they mean many things and get contextualized by other words. So despite being above jl bound, the model still forces a lossy compression.
next compression: each layer of the transformer blows up the input to KVQ, then compresses it back to the inter-layer dimension.
finally there is the output layer which at 0 temp is deterministic, but it is heavily path dependent on getting to that token. The space of possible paths is combinatorial, so any non-deterministic behavior elsewhere will inflate the likelihood of non-deterministic output, including things like roundoff. heck most models are quantized down to 4 even2 bits these days, which is wild!