Turing machines are deterministic if all their inputs are deterministic, which they do not need to be, and if we allow them to be. Indeed, by default, LLMs are by default not deterministic because we intentionally inject randomness.
If the brain exceeds the Turing computable, then all bets are off, but we have no evidence to suggest it does, nor that doing so is possible. This was in fact my original argument.
The only viable counter to my argument is demonstrating that there are computable functions outside the Turing computable, and that humans can compute them.