Earlier quoted context omitted.
But since its still on a permanent immutable blockchain, couldn't someone still trace Bitcoin/Eth transactions with perfect accuracy?
Yes - mostly. The idea behind a mixer is this: 1. Your transaction goes into their address 2. Their address is always transferring money to accounts. 3. Sometime after you pay them, some amount, not quite the same, leaves their address to an address you control, but which has no established connection to you. So an observer can see: 1. That you put money into the mixer. 2. The full list of addresses the mixer payed '…
In reality, you probably need to batch a few customers together: 10 customers putting in 1 BTC, 1 customer putting in 10. But these don't need to be long-lived groups, if the mixer has the volume. So "their address" would only be the same for a few customers. An attacker would need to constantly make transactions to determine the addresses involved.
Most mixers give you completely "clean coins": That is there's no transaction chain from your inputs to your outputs. So they are probably doing some sort of system similar to what I describe.