As an analogy, retro computers and consoles each have a particular “personality”. But does the fact that you can in principle emulate one on the other (subject to resource constraints) make them non-computers, just because this demonstrates their “personality” isn’t actually that fixed?
(I don’t think that human brains have such an emulation ability, due to their missing distinction, or heavy entanglement, between hardware and software. But that only shows that computers can in principle be more flexible.)