[stouset]

It's computationally distinguishable from noise iff you have the decryption key.

The key word here is "computationally". A signal encrypted with a non-OTP symmetric key can be distinguished from noise without the key — unfortunately, for modern key sizes (128, 196, or 256 bits), the cost of doing so is prohibitively expensive for even arbitrarily advanced civilizations, unless (as Brice Schneier put it) they are building computers out of something other than matter that occupy something other than space.