Unlike most other Americans, I actualy paid attention in sex-ed:
8 Fascinating Placenta Facts | The Pregnancy Companion
The disc’s attachment to the uterus is where the maternal blood and baby blood exchange oxygen and nutrients. The mom’s blood and baby’s blood DO NOT TOUCH. The umbilical cord is attached to the placenta and it carries these nutrients directly into the baby’s blood stream. The amniotic membranes (bag of water) adhere to the placenta as well as the uterus.
Note "
adhere". If you put a sticker on your arm, that sticker does not become part of your arm. It's just sticking to you. Same thing.
The placenta is not a part of the woman's body. It's stuck to her, touching her for a time. Her blood and nervous system do not enter it. It is not a part of her, it is simply inside her. In real estate and construction we call this an easement or a right-of-way.