I just tested these claims.
I modded cats to melt on embark, producing puddles of cat-syndrome-laden-goo. The cat syndrome targeted the eyes and the heart with advanced rot (taken from the GDS syndrome). I also modded out shoes from the dwarf entity.
On my test embark, the cats died and the 4 dwarves who rushed over to clean up the puddles became infected. I set up a hospital and let the doctors go to work. All of the starting 7 were full doctors. After the "Diagnosis", there was a short bit of "Surgery", followed by the "Remove Rotten Tissue" job. After the doctors left to clean up, the medical charts for the dwarves had "Rotten tissue excised from left eye". The dwarves had scars on both eyes, which were blind since most of their tissue was excised. The heart was still rotten, had no surgery performed on it, and was not amputated. The eyes weren't even amputated, just cut apart.
I'm calling BS on doctors killing patients. In DF, there is neglect, but there isn't malpractice.
Just to point out a few things:
1. Hearts aren't vital organs in DF, yet. Heartlessness is just fine. Getting a rotten heart just causes some bleeding.
2. If the docs were skilled enough diagnosticians, maybe they realize cutting out vital organs or ones with lots of major arteries is a BAD thing.
3. You can't cut out eyeballs in Adventure Mode, maybe the same concept applies as a bug for surgeons in Fortress Mode?