@layman,
If you distinguish the message from the messenger, then you ought to agree, not disagree.
Lots of radio transmissions from natural sources and as the byproducts of artificial processes contain elements of complexity, regularity, and repetition or redundancy. They aren't messages, though. An objectively indistinguishable signal could be a message, but only if an isomorphism such as I described is created.
One doesn't have to insist that the ink spots disappear if they aren't observed; but one does have to insist that ink spots are no longer text if they are incapable of being read or if nobody recognizes them as such.
Let's use the example of a one-time pad, which is a theoretically unbreakable cipher system (that is, it is unbreakable in theory, not just in practice) which was once used by Cold War spies. (Sometimes it was misused, which allows it to be broken, hence the Venona Project.)
The system consists of a polyalphabetic substitution cipher married to a pad of pages each of which contains a random key which is as long as the plaintext message to be sent; and (very important) each key is used only once, with a single message, then torn off and physically destroyed.
If I encipher a message this way, it will be indistinguishable not only from random noise, but also from every other possible message of the same length. In fact, using the wrong random keys, it is possible to generate every possible pseudo-message from that ciphertext. Consider the result of writing out every possible permutation of letters having the same length as the ciphertext, and you'll have a good model for the number and variety of plaintext messages that can be extracted. Some of them are wholly gibberish, some only partly, and some are wholly intelligible. But only one out of countless possibilities is true.
Only I know the key. If I cease to exist, is the ciphertext a message? It's true that, using the correct key with the correct polyalphabetic substitution cipher allows a message to be extracted. But so does using the wrong key. It just extracts the wrong message. And there are a potentially unlimited number of extractable messages, since there are not only a very large number of potential keys and ciphers, but also a very large number of coding systems which can be used to make plaintext number groups represent letters, syllables, words, sentences, or general ideas; and also a very large number of languages they might be expressed in, including entirely arbitrary (but coherent) fictional languages each with its own grammar, syntax and vocabulary.
By now it should be clear that the "message" is a set of abstract relations, not something intrinsic to the ink on paper. And it exists only for me, and only as long as I do.