Where I don't think your argument fits is that it could be applied to things LLMs can currently do. If I have an insufficiently trained model which produces a word salad to every prompt, one could say "that's not a malfunction, it's still applying weights."
The malfunction is in having a system that produces useful results. An LLM is just the means for achieving that result, and you could argue it's the wrong tool for the job and that's fine. If I put gasoline in my diesel car and the engine dies, I can still say the car is malfunctioning. It's my fault, and the engine wasn't ever supposed to have gas in it, but the car is now "failing to function in a normal or satisfactory manner," the definition of malfunction.
I'd argue that's what an LLM is, not its purpose. Continuing the car analogy, that's like saying a car's purpose is to burn gasoline to spin its wheels. That's what a car does, the purpose of my car is to get me from place to place. The purpose of my friend's car is to look cool and go fast. The purpose of my uncle's car is to carry lumber.
I think we more or less agree on the fundamentals and it's just differences between whether they are referring to a malfunction in the system they are trying to create, in which an LLM is a key tool/component, or a malfunction in the LLM itself. At the end of the day, I think we can all agree that it did a thing they didn't want it to do, and that an LLM by itself may not be the correct tool for the job.