If you go back to Shannon's original paper in 1948, you'll see that in positing the theory he implicitly, if not explicitly, built in the context with one of the few diagrams (top of page 2) which appears in the paper as part of the overall engineering problem. The diagram of which I speak is the one that physically shows what are all now commonly called the source, the encoder, the channel, the decoder, and the receiver of the message. In your question, you're simply changing your decoder and receiver, but the information from the source/encoder which travels through the channel are exactly the same. Thus, the DVD still has the same amount of information encoded on it, it's just that your "new decoder" is only capable of giving you a 0 or a 1 indicating that you either have the disk or not. With the more sophisticated decoder, you obviously get the full message back out of the system.
Taking this all a step further, we might now say from a philosophical standpoint that Shannon has also answered the question "if a tree falls in the woods, and no one is there, does the tree make a sound?" If nothing else, it has at least certainly sent a message!
(The careful reader will also notice that in paragraph two of the paper he specifically states: "These semantic aspects of communication are irrelevant to the engineering problem." This specifically partitions out errors in which a message is perfectly sent and perfectly received, but the proverbial person at the other end misinterpreting the actual semantic meaning.)