I don't think it's fair to say their point is incorrect. If you're talking in absolute technical terms about what "a blockchain" is in the abstract then, sure, a blockchain is immutable... but cryptocurrencies don't use "a blockchain" they have "the blockchain" and "the blockchain" is just whichever blockchain the network has decided is the blockchain. For all intents and purposes, "the Ethereum blockchain" is mutable because it can be swapped out if everyone agrees.