Just a note regarding my own experience. I believe the actual question of the Church’s stance has been answered. I attended medical school July 1993 through June 1997 at University of California, San Francisco. Christians were treated dismally and were regularly insulted for their faith in classes and small groups. However, the anatomy lab had extremely strict codes of conduct. The cadavers were to be treated with the utmost respect and, when finished, the option was given to hold a memorial service, inviting the family members.
When I first entered the lab and was assigned to my table, I looked at the body in front of me and had a lump in my throat that made it hard to swallow. The first thought I had was "This is someone’s mother; someone’s grandmother! Someone is out there grieving the loss of this person and I am about to cut the body in to pieces. Eventually, over the course of my studies, I developed a profound respect for the generosity of the person. I would walk in to the lab and say “good morning, Grandma. What are you going to teach me today?” Of course, I knew the truths of the situation, but this was my way of dealing with the emotional impact the lab requirement had on me.
I know there have been stories of awful and disrespectful acts in medical school anatomy labs. However, I believe, most medical students shared, at least to some extent, my experience. Awe and respect for the enormous generosity of a person who contributed more than any professor anywhere to my education and my ability to understand, in some small way, the human anatomy and how to apply that to the healing arts.
I hope that adds a little comfort to any questions you may be having.