I can't speak to everywhere, but in Kenya (the funding in the OP was for a Kenyan) many of the charity medical facilities are run by religious organizations, who recruit religious medical professionals from abroad to volunteer their time and services. If an OB/GYN happens to be volunteering the person could very well receive a C section. They also have stockpiles of various drugs which they've received from donations, so they could get an epidural if they happened to have the right stuff in the stock room.