It's true and not true. If you're not careful, you can get identified even while using cryptocurrency because the ledgers are all public. If anyone can figure out that you're tied to a single one of your historical transactions, they can trace everything your "wallet" has ever done. But if you use single-use wallets, crypto shufflers, whatever else the kids have going these days, you can be untraceable. The easiest way to do private crypto is to use Monero, which automatically handles most privacy concerns.

Edit: A small vid on monero: https://www.youtube.com/watch?v=B7sLnmlZ-kU

I'm not immersed in the cryptocurrency world day-to-day so if anything has changed lmk