Yeah, you can be traced if they KYC.
Purse.io doesn't KYC, and there is no direct link between your ID and the crypto.
How it works is you pay for something off a person's amazon wishlist, and they give you crypto in return (held in Escrow). The tradeoff for privacy is that you have to take a discount, usually around 20%. However, like I said you have no direct link to you buying Bitcoin or Bitcoin Cash and any government ID. (You can even buy Amazon giftcards to buy the crypto in cash at a store, instead of using your card.)
Then you can use Bitcoin or Bitcoin Cash to trade for other cryptos via atomic swaps (e.g. Changelly or Simpleswap).