Of course you can know if you have the wallet data. You spent it. Is that so different from grabbing two lightning wallets, seeing a payment for X sats at Y timestamp and concluding you have the sender and receiver wallets?
Personally I don't see that as a flaw.
As for knowing true spends on chain, that's the thing, you can't.
All you can say is a certain output is part of a ring signature. You don't know whether it's a decoy or a real spend.
Could this be improved? Yes, and it will (FCMP++ soon™).
Are a few statistical attacks around this weakness known & understood? Yes.
So.. his arguments are a nothing burger, really.