AES-128 keys unique for fixed plaintext/ciphertext pair?

[Ralf-Philipp Weinmann]

I was wondering whether the following is true:

"For each AES-128 plaintext/ciphertext (c,p) pair there 
 exists exactly one key k such that c=AES-128-Encrypt(p, k)."

Of course we can look at the generalized case of Rijndael
with block size == key size and ask the same question. I'd
be happy with an answer for AES-128 nonetheless.

At first I thought this was a trivial question since the round
function minus AddRoundKey is bijective. But I haven't been
able to come up with anything thus far, so I thought I'd
ask the list.

Any ideas?

Cheers,
Ralf

p.s.: I am familiar with Wernsdorf's paper, but it hasn't
      helped me thus far.

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