I understand is possible to do operations on encrypted data (which results in an encrypted result) all without having the key to the data (or the result), and maybe there's a way to do this to allow the duplication.
If there is it could (but shouldn't ?) be used.
The issue here, to me at least, is that someone malicious that has exactly the same data could encrypt it and then verify the above.
It's also highly experimental at this point, from what I remember.
[1] As a trivial example, let's say you give me a very large number, and your encryption scheme is to add some number, n, of zero bits at the end. Only you know how many bits you're adding - n is your private key. Regardless of what you pick for n, I can multiply your number by 2 (i.e. bit-shift it) and give the result back to you, which you would then be able to decrypt to the result of the calculation.
This works for any value of n, so I can't tell if two original numbers are the same by inspecting the ciphertexts.