Special equivalent key in symmetric encryption
Yes. Actually it is quite likely that there are quite a few such keys for block ciphers. That said, finding one takes a collision search which may take a lot of time, especially for ciphers with a large block size.

Proving that there are no other messages that permite to the same ciphertext may even be computationally infeasible.

It would not be a good property for a block cipher to have keys that are fully equivalent. It may not directly destroy all trust in the cipher but it would certainly raise a few eyebrows.