I don't know for sure, but I think you're right.  Our body is not ours to donate.  

When my father died we let them have his eyes for medical practice. How else is a medical student going to learn properly? It would be just as foolish for me to not let the medical students examine my gallbladder after it was taken out, just because it was a part of my body. They aren't going to desecrate it. Let's not get too scrupulous. In fact I thought it was a good thing that may help a future patient. If I donated my body to medicine (although I don't know why they would want this broken down husk), I wouldn't mind. My family doctor would make sure it would not be used for nefarious purposes, only education.

Or would you like new doctors practice on you (with living organs) instead? I would like my doctor to have at least some familiarity with an organ before he started in on mine.

Oh and that rules out a body never having an autopsy either because they often examine the body, cutting and so on, sometimes with intense examinations, and organ removal, occasionally with new doctors observing and learning as well. As long as the body is disposed of properly -- family requests and burial, there shouldn't be a problem.

My main concern would be with organ donation and the necessity of having a living body from which to harvest the organ.  There is a question about the definition of death from a medical and ethical standpoint.  The concept of brain death is a new one and it has facilitated the doctor's ability to take organs from what they define as a person in a vegetative state, with a functioning heart and respiratory system.  

When my father died we let them have his eyes for medical practice. How else is a medical student going to learn properly? It would be just as foolish for me to not let the medical students examine my gallbladder after it was taken out, just because it was a part of my body. They aren't going to desecrate it. Let's not get too scrupulous. In fact I thought it was a good thing that may help a future patient. If I donated my body to medicine (although I don't know why they would want this broken down husk), I wouldn't mind. My family doctor would make sure it would not be used for nefarious purposes, only education.

Or would you like new doctors practice on you (with living organs) instead? I would like my doctor to have at least some familiarity with an organ before he started in on mine.

Oh and that rules out a body never having an autopsy either because they often examine the body, cutting and so on, sometimes with intense examinations, and organ removal, occasionally with new doctors observing and learning as well. As long as the body is disposed of properly -- family requests and burial, there shouldn't be a problem.

As someone who was both a coroner and a teacher of forensic medicine for decades, I can tell you that your family doctor will not have any say as to how the body is used.  Bodies are stored in the cadaver lab at the medical school (which is generally part of the Department of Anatomy).  When all of the required dissection has been done, the body is cremated and the ashes either buried in a common grave with the ashes of other donors or returned to the family.  In an anatomical teaching hospital, there is, frankly, sometimes not too much left for burial.  And yes, that is how we learn anatomy and physiology, but I myself would not be comfortable with being a donor.  

From Audio Sancto: May We Donate Our Organs