To fix the analogy, consider circuit-bending a handheld transceiver. Assuming the "thinking" / "free will" part represents the conversational partner on the other side of the radio link, modifying my transceiver can alter not just how I hear my partner's transmission, but what my partner receives from me as well. Being able to modify the input, I can influence what my partner will say next.
The brain has a lot of inputs (a very important sense group is the so-called "interoception" - the sense of your internal body state), all of which send telemetry completely under the radar of the conscious mind. Only few of those signals surface explicitly for a mind to introspect, but the rest still influences how the mind thinks. For instance, it may take many minutes before you realize your suddenly irrational behaviour is just a sign of hunger.
My conclusion is this: even if you believe (against Occam's razor) in the mind being a separate, remote phenomenon, and the brain being just a transceiver of some information carrier we have no first clue how to detect - the brain still seems to be the single point that collects the inputs and outputs of that communication. Essentially, it could be seen as an electrochemical I/O module, connected to the mind via Magic waves. There is zero functional difference between this model and (simplified, Occam-friendly) the model in which there is no remote mind, and the brain is just the whole computer.
(And, unless you can show that "remote mind" vs. "brain mind" have different testable predictions, there's zero basis to believe in the "remote mind" version, no matter how much more philosophically comfortable it seems.)