Almost, i mean even if you buy any privacy coin and you want to buy any other cryptocurrency with it, you need register to some exchanger site first though, and exchanger site mostly need some id verification or something like that so you can withdrawit to you bank account. The conclusion is if you still use your real id in any exchanger you use, there no thing such privacy.
I think there are withdrawal limits where you will not be asked for I.D verification, anyone choosing to stay anonymous can decide to stay under those limits using multiple accounts. It might sound tedious but it's one of the sacrifices one can make for privacy.