Preventing double spending is a feature of the consensus mechanism indeed, if it is augmented with other rules (longest chain wins), but immutability does not rely on it, as I said in the comment you are replying to.

EDIT: I've updated my previous comment to make it clearer that what I'm saying is "PoW is not an immutability mechanism" (to which answering "you are wrong, PoW prevents double spending" makes little sense).