The zerocoin mixer can be periodically reset, forcing all anonymous zerocoins to cash out periodically to basecoins which can be re-minted into the next instance of the zerocoin mixer. In this way, it can be proven that no zerocoins were created out-of-thin-air. All the anonymous mixing that occurs in the zerocoins can remain fully masked because the zerocoins balance can be merged before un-minting back to a basecoin.
So the problem is easily resolved. And the anonymity is not compromised even if the master private key was.
The process of resetting the mixer and forcing people to remint does compromise anonymity. If you were an adversary and wanted to spy on zerocash users, forcing such a reset (and then spying on them while redeeming and reminting) would be precisely one way you could go about doing it. This general pattern is a classic exploit method (e.g. force/trick user to reset password; intercept new password, etc.).