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).
If you can perform arbitrary computations on the encrypted data (yielding encrypted results) then I think you can take advantage of that to encrypt whatever you like.
The idea is to evaluate a constant-valued function “inside the encryption”, e.g. the function that ignores its input and always returns ‘A’. The result of that will be an encrypted version of ‘A’.
This argument is valid... the flaw in the author's logic is rather the assumption that encryption is a function, i.e. that it is deterministic. In fact decryption is deterministic, but encryption is not, and that's what prevents this kind of attack. Yes, you can obtain an encryption of any given ASCII character using a constant-valued function "inside the encryption", but the important point is that it's just an encryption, not the encryption, of that character. The decryption function, which you do not have access to, will send all possible encrypted representations back to the same plaintext.
