That holds if the preferred method of transfer is "uploading", yes. But what about a more gradual method?
Suppose that rather than wholesale uploading your brain, the process were to start with an implantable (or even wearable) computer that interfaces directly with the brain, perhaps providing extra sensory data or storage space. Over time, the mind learns to make this integration seamless, partly integrating with the device.
At this point, a second device is added to the mix, providing some additional functionality, and the person learns to integrate with this as well. The cycle repeats, adding more and more devices, and the person learns to integrate with them more deeply.
Eventually, one might learn to "inhabit" these devices: integrating so deeply that the brain itself becomes unnecessary, like a vestigial organ. The person might go back and forth on several occasions, to build confidence both in the procedure and to build confidence that no matter what "side" of the brain/computer divide you happen to be on at the time, you are still you. Depending on how the technology works, you might even be able to learn how to "transfer" from one set of devices to another, likely starting from similar principles, though the process could be accelerated.
At that point, the last step is simple: inhabit the devices and do not go back. Once your body is disconnected from the system, you're "in" for good.
I'm afraid I don't recall the story where this concept originated, but I thought it was intriguing as a description of an "uploading" process that did not involve making a copy. Does anyone know what it might be?