brain transplantation -- impossible? really?

I was at a barbecue a while back with mostly med students, and the topic of brain transplantation came up, initially as a joke but it quickly turned into a debate of theory.

Medically speaking brain transplantation is, as we currently know it, an impossibility, as argued by most of those who were in the room at the time. For one, there's the inevitable, unavoidable displacement of the brainstem, among various other issues like what would happen to the donor's memories, personality, identity, etc., and so forth. Seemingly an endless list of reasons to support their argument.

And yes, I accept their premise and the undeniable sense of impossibility given the world we live in today, BUT what I believe is that it would be utter hubris to think we could, at this moment in time, declare something to be medically impossible, full stop; to think we know enough right now to say, "there is no way _______ could ever happen." I mean, who would have believed you if forty years ago you told them heart transplantation -- when a person's heart is stopped, removed, replaced with the heart of a complete stranger, then restarted -- would not only occur but become commonplace in any cardiothoracic surgical ward.

I believe one day brain transplantation, in some form or other, will be possible. I'm not saying in my lifetime, or in two lifetimes, but that one day there will be a headline of the sort. Because honestly, I just read an article today entitled "Baby born after mum declared brain-dead" and I wasn't even that surprised.