I would say you pretty much have it correct. KYC laws are essentially attaching an identity to a particular wallet that you own and chain analysis companies can track the movement of those coins on chain.
So if you have a wallet that you have moved coins from Coinbase onto that's only one or two hops removed from your initial wallet on coinbase It's pretty trivial to track the movement of those coins. And if you add "non-KYC" sats to that wallet, you are proving that you own those sats to whoever might be watching.