Not going to carry on, we can disagree. But I don't understand how you can say that. I'll the analogy I raised earlier:
An AM broadcast is not exactly equivalent to the program material.
This point is important for the person designing the receiver.
If the person designing a receiver (or trying to fix one) needs help understanding, it's important to be able to tell them the details of the modulation and the frequencies it creates. It does not help them to say it's exactly equivalent to the program material.