This isn't a disproof. Just as the radio is an instrument that plays music from the outside environment, a brain is an instrument that behaves in response to the outside environment.
The existence of radios shows that being able to interfere with a signal locally via one mechanism (interfering with the radio electronics) doesn’t entail it’s generated locally by that process — the local process can merely be translating between media, eg light and sound.
Unfortunately, this pokes a hole into the logic that thinking is necessarily local, because it was depending on clinicians interfering locally to show that brains are a local phenomena — but that reasoning doesn’t apply generally, eg, in the case of radios.
You’re correct that we know the brain is going to be doing some kind of transducing, but that doesn’t mean it’s doing the thinking — it could merely be a relaying device between whatever generates thought and the body, like a radio translating between EM and sound.
