As for our alleged anonymity: we stopped being anonymous quite a while ago when our policy changed. We don't advertise ourselves as anonymous and it is stated in our FAQ, Terms of Use, and Privacy Policy. All our customers automatically accept them when using ChangeNOW.
Initially, you marketed yourselves as an anonymous exchange and that was what most people used your service under the impression that your service guaranteed anonymity.
I think that this is misleading advertising at best and very shady business operations in general.
Why are you not able to return the funds which Privcoin sent you back to the same sending address? Since you are not exchanging any funds but rather just conducting a crypto to crypto transfer, to the best of my knowledge, that should not be something that is illegal in any state. I would also trust that Privcoin's claim that there are no specific legislation preventing you to complete the exchange to be true.
Anyhow, seems like all of these instant exchangers (shapeshift, changenow, changelly) have all become stricter with their KYC with Changenow and Changelly's reputation being much worse. I would be extremely careful about dealing with all of them.