I'm not sure of the details to be honest. Certainly if I want to change normal US$ in a bank into USDC then I have to go through KYC etc. If I then transfer it to a private wallet and then send it to someone else's wallet for an iffy transaction they'd see on the blockchain it was me but not necessarily who the other wallet was.

A way to make it less traceable is to transfer it to an iffy crypto exchange, change it and then withdraw it somewhere else. Some of those are not very good at keeping records and the like. Like I use mexc who can change usdc and when I wanted to do my tax return they said they couldn't retrieve transactions over 18 months ago - they delete the data they say. And mexc isn't the worst.