In theory, ECAF could effect the immutability of the blockchain depending on what precise point they intervened.
No, this is not possible even in theory. If the immutability of a blockchain is broken, there is some serious bug in the software.
This is how it should go: Transaction is recorded on the blockchain. A dispute arises considering that particular transaction. An arbitrator looks at the case and makes a ruling (which is recorded on the blockchain). A new transaction based on that ruling is proposed to the network. BPs check that the proposed transaction comes from a real arbitrator, etc. and accept it to the blockchain.
All transaction are recorded immutably on the blockchain: original disputed transaction, arbitrator's ruling, and enforcement of the ruling by BPs. Nothing is removed from the blockchain, only new transactions are added to it. Just like a blockchain is supposed to work.
This is semantics. My fault for not explaining fully in the above reply.
If an ECAF arbiter incorrectly rules on a case and orders the reappropriation of funds to another party, then it effectively interferes with the immutability of the blockchain. Yes, the blockchain code isn’t reversed in any way, but the outcome – the result the person who thought they had sent an immutable transaction in the first place - is being modified (by the arbiter) after being created, therefore the intended result becomes mutable.
My point is that talking about immutability of a blockchain in this kind of case doesn't make sense. The technical immutability is preserved, and on the level of token amounts the concept of immutability doesn't apply because everything is done by the rules.
If an account is a multisig account, like every account is in EOS, then everyone who has the keys to the account has an ability to do transactions.
So rather than speaking about "immutability", we should be speaking how to make the system fair, transparent, etc. so that all parties can trust it.