We all understand the logic that both of you are following. And if you want to have a discussion that follows some kind of rules of debate and logic, you are both right. We who have some kind of connection to "radio" understand that.
Maybe radio has done a poor job of "industry protection". We don't have the kind of junk-yard dog mentality that is needed by a good copyright or patent or trademark lawyer.
For the rest of the world.... people who don't own a part of a radio station, people who never worked in a radio station, people who wouldn't recognize a radio station sitting beside the road if they drove past it, "radio" is used simply to describe an audio source.
Got the sniffles? You turn to your wife and you ask: "Do you have a Kleenex?" What you want is a tissue or a handkerchief. You don't really care if it is store brand, a napkin from the last visit to McDonald's, or a genuine Kleenex.
Sitting in someones office you are handed a document that you find interesting. Unless you are a salesman of reproduction machines, you are likely to say: "Can I have of Xerox of this?" You are not going to be concerned whether the COPY is produced on a Konica, a Minolta, a Xerox or a Brother. You just want a reproduction.
If I have allergies, I may be very, very specific about what kind of cellulose product I want to use to mop up my sniffles. If I am an artist with the kind of color-consciousness possessed by the woman I am married to, I may enquire about the variety of the reproduction machines available in your office and I may be very, very specific about which machine is used to copy the document.
Radio seems hell-bent on eliminating every ingredient of programming that could make it different than Muzak, Pandora, in-store retail-audio a-la-Walmart or a $19 mp3 player. What is the industry doing that would cause Joe the Plumber to think there is a distinction?