Over the course of my career I’ve spent over thirty years working in various developing countries trying to better understand and fight infectious diseases. One of the things that alarmed me most was that in many places, parents and caretakers didn’t even have a word for diarrhea. Sadly, this wasn’t because diarrhea was rare. On the contrary, diarrhea was so common that it was seen as a normal part of early childhood, and thus didn’t need a name.
No doubt Dr. Brewer has been doing a wonderful job bringing public-health research and services to the third world. But he himself is suffering from an acute case of the highly-infectious "no word for X" trope, and our generic advice about metaphorical hygiene applies: If someone tells you that one or more languages have no word for X, or if you find yourself using this figure of speech to make a social or cultural point, you should seek metaphysical treatment immediately.
It's hard to know exactly what languages Dr. Brewer has in mind, but he mentions Mali, and an online English-Bambara dictionary has
Chuluka ~ Diarrhoea ( have diarrhoea )
Swahili is a sort of lingua franca in the area, I believe, and Charles Rechenbach's 1967 Swahili-English Dictionary has
harisho (ma-) 1. med. diarrhea.
The strangest thing here is Dr. Brewer's logic: among the many things that are a normal part of early childhood, and for which many languages including English nevertheless have words or phrases, are babbling, crawling, diaper rash, burping, suckling, smiling, …
I'll leave it to readers to find the words for diarrhea in various other African languages.