Bills shit claim. First of all SW coordinator is blinded run over tor and CoinJoin coordinators are simply message passers. They simply pass data packets to connected clients. Clients never surrender custody to any 3rd party. Clients collaborate w/ each other, and for equal outputs to exist there will be doxxic change and coordinator is blinded (soon decentralized in SW) It doesn't know the links between a coinjoin's inputs and outputs. That was one of the major goals of the zerolink framework. Also doxxic change is completely unaffected by mixes since it has never been mixed. And it sits in the separate derivation path (sparrow wallet)

Every SW user knows exactly what to do with that doxxic change so there is no combining with other doxxic change that didn’t come from the same source. Software freezes these change utxo so one cannot accidentally spend or combine them.

The Tx0 makes all your UTXO's share a tx hash, which prevents them from mixing with each other, preventing an "accidental" Sybil attack from entering a large amount of BTC, Samourai wallet software separates the coordinator fee in the Tx0 no fee flagging in the fee addresses. Every communication between Alice and the coordinator is made with a different Tor identity. It's transparent for the coordinator if one of the messages is actually sent by Bob, so when Alice sends her clear output to the coordinator it's made with a Tor identity different from the Tor identity used to submit the input and the blinded ouput. Who is using this Tor identity is transparent for the coordinator. It’s two separate Tor identities. This was even in the original zerolink docs.

So once coins are mixed, they are segregated and can't "accidentally" make their way back to unmixed section of wallet. You have to manually generate a receive address and send from postmix to get utxos back there, which obviously you shouldn't do. This is the only way to have true ZeroLink, where a user can't spend mixed and unmixed together. This is not happening in wasabi or joinmarket.

SW doing ZeroLink original spec, which is simultaneous denominated pools, max entropy mixes for the number of inputs/outputs, never 2 or more same previous tx in a same mix, and unequal amount coinjoined spends post-mix if the user chooses.