This is not a true statement. CC may leak information about the plaintext in ways that KC can't handle, even without breaking it. For example, applying CC might deterministically affect the message length.

One of my favorite cryptographic attacks ever was of this form, known as the CRIME attack [1]. It was a "partial plaintext" attack, where the "CC" in question was plain old gzip. Basically the attackers controlled a small part of the plaintext (for example, a field in an HTTPS request they could send with CSRF) and they were able to use known properties of the CC to get some information to leak into the message length -- namely, if the message fragment they controlled appeared elsewhere in the request, the gzip encoding would be shorter, and hence the encrypted request would be shorter. This is something that happens even with a "perfect" KC that no one could break.

[1]: http://en.wikipedia.org/wiki/CRIME

This is one of the defining characteristics of cryptography to me -- there are no perfect cyphers, there are only good systems. Littering extra cryptography around nearly always decreases security. The most secure system is the simplest system that works.