a third party can voluntarily surrender complete control over what is going on. they can issue a token for something, for example a $10 dollar bill but do it in such a way (blind signature) that when you go to spend it they cannot connect the spend to the bill they issued.

if you want to do it without a third party you end up with something like zcash. monero plans to follow suit (currently only the amounts in monero are zero knowledge).

That can leak information to the third party that you may not want them to know.