This is a very interesting thread. i don't usually comment in off-topic forum discussions, but this one got me. My "day job" is as an anthropologist studying virtual worlds. The anthropological vocabulary used around the issue raised in the opening post has two key terms - "embodiment" and "habitus".
Looking at embodiment for a moment points up one way in which this is not a binary (either/or) question. "You hurt me! You broke my arm!" If someone said that most of the time we wouldn't even pause to think about the implications. Yet that simple statement contains both identification of self with the body and distinction of self from the body. Once the question of how intertwined are my body and my sense of self is made explicit then there is a whole range of issues to address. All of which bear on the initial question. Here's just one example of how profound the question is:
If I get a blood transfusion is that blood then part of my body and therefore part of me/mine? How about a transplanted organ? If I have a permanent cochlear implant to aid my hearing is that part of my body and therefore me/mine? How about a prosthetic such as an artificial limb? Is a wheel chair a prosthetic in the same sense? What about an automobile? On first thought my hair and my fingers are equally part of my body. But getting a haircut and getting a finger cut off affect my sense of self quite differently.
It's smeared out along the spectrum - and not everyone will put the smear in the same place within their mental model - but somewhere in there is a shift from "me" to "not-me". There is also a shift from "my body" to "not my body". And those two shifts don't necessarily happen in exactly the same place.
Habitus is a much more difficult term to explain simply. Habitus has to do with the way that outside forces determine how we are allowed to express ourselves through our bodies, and how our bodies determine our sense of self. There are plenty of movies around that use the body-swap motif for comic effect. But there are also real-life situations in which wearing different clothes,changing postures, gestures, etc. are critically important. For example, when i lived in another country I began to dress, walk, talk and so on like the people who were born there - more and more as time went on. To the extent that people from my own country did not recognize me as one of them and would try to talk to me in a "foreign" language that was awkward for them, and were shocked when I fell back into the habitus of my homeland - revealing me as "one of us". I say I changed habitus because my posture, gestures, tone of voice all changed, not just the switching speech back to my first language. But it's much deeper than that. How we walk and talk is affected profoundly by how we were indoctrinated by parents and others - from before we we were born in many cases. Our sense of self is being molded at the same time, by the same people, through the same experiences. Most of that indoctrination we are no longer aware of. We don't usually stop to think "who am I if i wear this shirt?" or "am I truly chewing this food as my innermost myself, or because this is how I was taught an -------- chews?" If innate posture, vocal expression, and a thousand other things I'm not aware of influence how I experience myself as being in the world, and those things were imposed on me by other people's sense of what the proper way for my body to be is, then to what extent is my body me? When my body is in some way an imposed constraint on myself over which I have no control is it still me? Or is my body a prosthetic I'm more or less permanently attached to?
No easy answers to those questions.
Both embodiment and habitus touch on the issue of "presence" as well. Most of us are comfortable talking with someone who isn't in the room - maybe isn't even on the same continent. Someone we are in a skype call with has a presence the room, but are they present? We are not many years at all (probably less than 5 according to engineers I've talked to) away from remotely operated presences that are visually a lot more like full bodies than like claws on the end of a crane. People already experience vertigo in a virtual environment when they lose a sense of connection to their body because in effect they have two bodies in two separate locations and they are not sure where "they" are. When being "here" and "there" simultaneously is as common for more or less full embodiment as it is now for conversation all sorts of perspectives will change, some overtly and some more subtly. And it's not such a far step from there to putting the "body as shell" question in the context of a culture in which we can change bodies thoroughly and for an extended period of time if not permanently.
"You look different" is what we say when someone dyes their hair or grows a beard. We still think of it as the same person. But what about when it's a whole different body? Unless it's a perfectly identical clone a different body = a different habitus. Can it even be the same self in a different body? If it's not the same self, then what was it that got transferred? If it is the same self, but a different body, and we still say "you hurt me" when someone breaks our arms then what does that mean about self/body ?
I don't know specific detailed answers to these questions. I'm not sure there is one singularly correct answer. On a personal level there are times when my sense of self and my body are quite isomorphic if not perfectly identical, but there are other times when they are very distinct, but still overlapping.