Bob, I can't disagree with your interpretation of the words in the NEC, especially since I'm the one who wrote "Charlie's Rule" in the first place. But something is not quite right here. Perhaps that means that the code was not written well, and that a clarification is needed. I suspect that the intent was that the "individual branch circuit" mentioned in the exception to 250.52(B)(1) should supply only a simplex receptacle. You correctly point out that that is not what the words say. Nevertheless, I believe that is the requirement the CMP meant to impose.
Speaking philosophically, and for the moment discounting the possibility of DIY work, I believe that a homeowner can never, NEVER create a code violation by virtue of using electrical appliances and equipment. Let's suppose that I design the home's electrical system, Bob installs it, and Larry inspects it; then Joe and Jane Homeowner move in. Lets suppose further that they possess no tools, and would not know how to use them anyway. All they do is buy stuff at stores, and plug the plugs into the places where we have put things that can accept plugs. I submit that no matter what they buy and what or where they try to plug things in, nothing they can do can create a code violation. My reasoning is that 90.2(A) says that the NEC covers the installation of "electrical stuff," but it says nothing about the homeowner's use of the installation. If a violation is present, it means that the error was made by the designer, or the installer, or the inspector, or all of us. If I am wrong here, if the code is not written in this way, then I still think that it should be written in this way.
Here's my point. Lets talk about a 15 amp circuit supplying the fridge. As the code is written and as you have pointed out, you could put any number of duplex receptacles on that circuit, plug only one item in, and call it an "individual branch circuit." But then Jane Homeowner plugs in a second item, and now you have a violation. That should not be possible. The electrical distribution system should be designed and constructed in such a way as to make it possible for Jane to plug in anything she wants, and for there to be no resulting violation.
I conclude that if you have a 15 amp branch circuit supplying the fridge via a duplex receptacle located behind the fridge, and if an Inspector cites this as a violation of 210.52(B)(1), then I cannot call the Inspector wrong.