Death from bleeding doesn't come from tears anyway, you really don't lose that much blood from that. It's usually from incorrect detachment of the placenta from the uterine wall in some way. A lot of deaths are from placental abruption, where the placenta detaches too early, i.e. prior too or during labour. And then there are some post-birth bleeding deaths, where the uterus doesn't contract enough, or a piece of the placenta remains in the uterus.

Basically there's a large surface area along the uterus that you can bleed from, where the blood normally goes into the placenta, and during childbirth if the connection isn't severed correctly, you can bleed to death.

Today, if there's is an abruption that calls for an emergency C-section and blood transfusion, and they also give you a shot of pitocin after childbirth to help the uterus contract which reduces blood loss. They also check to make sure the placenta is whole and no bits have been left behind.

A lot of the infection reduction risks are mostly hand hygiene on the part of doctors and nurses. tl;dr graveyard tour guides don't know their obstetrics.