I didn't bother to read through the entire thread but I'd like to chip in my two cents anyhow. My understanding is that the continual process of unintentional rebirth is caused by clinging. Clinging to a self, clinging to views, clinging to sensations, clinging to any impression of reality as being "real" gradually forms mental habits that produce self-edifying illusions. Our habitual (read: countless lifetimes worth) clinging to a so called "physical reality" creates this physical reality. Put differently, the mind and the body are so closely interconnected because our current form is conditioned by that particular brand of clinging. It could arise differently, but that too would just be a differently conditioned illusion.
As Huseng noted, mind and body are infinitely divisible and neither can really be called discrete, self-contained entities. Clinging and karma govern how they arise in our experience, as very closely interconnected. Bear in mind that while altering the brain does alter the mind, altering the mind also alters the brain,as neuroplasticity goes to show. What's really at issue here is not whether mind and brain are the same thing, but whether or not the brain supercedes the mind, whether it produces the mind in a deterministic fashion. The fact that mental and physical alterations flow in both directions seems to indicate that this is not the case, not to mention pan-cultural accounts of spirits and creatures with a sentient mind and a non-physical body.
I am a lustful, angry dullard with no power of realization. Do not put anything I say into practice without first confirming it with a qualified teacher.