My understanding is that along with the addendum added to the post (having more than one possible representation of the same plain text for a given cypher), you also wouldn't be able to perform a re-encryption attack similar to how he describes. This is simply because to do that you would have to have the encryption key on the untrusted data center. Homomorphic encryption instead allows you to operate on the data without having either the encryption key or the decryption key (if it's an asymmetric cypher).