The idea with homomorphic encryption is that you can have the host perform computation against the cyphertext without decrypting it. They've gotten this to work, but it's still much too slow to be of practical value. It'll get faster naturally though, even if they don't actually refine the algorithms.
From what I can gather from this link they are just concentrating on encrypting the data stored in something like S3, and having an application that you've developed handle the decryption/encryption.
Actually, there are many cloud-hosted services that aren't HTTP services and could use such a framework as well. With plenty of power for homomorphic encryption.
There are certain special cases for which homomorphic cryptography should would acceptably. Blinded signatures are one example of something essentially a special case of it.
IMO, the right way to do hostproof is some combination of trusted computing (HSMs, TXT, etc.), protocols which can prove things clearly but not keep them confidential (like bitcoin -- something which used certifications to prove source code hasn't been altered and compiles to the binary you're talking to would be a great leap forward), special-cases of homomorphic crypto, and client side execution (either all the time, or for some statistically significant subset of operations, to catch cheaters eventually).
What makes you say homomorphic encryption doesn't have a chance of working? I grant you that it will be at least 15 years before a commercially viable homomorphic encryption product is released, but to say it has no chance of working is silly.
My research advisor likes to tell a story of his friend going to see Rivest give some of the first lectures on RSA circa 1977. All the systems people in the room laughed at the naivete of this young cryptographer and his hope that such an absurdly slow encryption method would gain widespread adoption.
