Some of the stuff that happens to the body clearly impacts our states of consciousness. Blood-alcohol levels, for example. So if I take your statement at face value: OK, so you simulate at least some of the rest of the body, perhaps all of it. So what? Still a simulation.
You can also think of it this from the opposite direction, where someone might try to argue against a purely material origins of consciousness by saying "the brain doesn't work if you take it out of the body" — that this is in fact true, doesn't mean the brain isn't the bit doing the thinking.
You can take Searle's position (why yes, I do have a philosophy qualification, albeit a mediocre one): "No one supposes that computer simulations of a five-alarm fire will burn the neighborhood down or that a computer simulation of a rainstorm will leave us all drenched."[0], but that only works if a mind is a substance of its own kind rather than the emergent result of the processes that gave rise to it. The components of a simulated rainstorm will still interact with each other as those of a real one, if given sufficient fidelity.
Perhaps minds are emergent from some quantum shenanigans, as Penrose says[1]. Then it would take a quantum computer rather than a classical one[2].
> I wonder if Black Mirror ever did an episode about someone unwillingly personality-cloned into a computer, then killed, with everyone around him acting as though this were normal and he — still conscious — was a non-person?
What you describe is a P-zombie, and as https://en.wikipedia.org/wiki/Philosophical_zombie will show, there's no consensus over this even amongst philosophers.
[0] https://en.wikipedia.org/wiki/Synthetic_intelligence#:~:text...
[1] but it would be horrifying if he's right specifically about microtubules, because those are in basically every living cell, and hence if they do mediate consciousness then potatoes would be conscious: https://en.wikipedia.org/wiki/Orchestrated_objective_reducti...
[2] While it's technically possible to simulate quantum processes classically with an exponential slowdown, those kinds of technicality also make the entire universe and everything in it into a Markov chain, I prefer to only point out such things to show the limitations of making such arguments.