In Japan, taking a bath is somewhat of a luxury, because heating water is expensive. Most of the time, they only take showers. If there's a bath in the house (usually a small tub), multiple persons in the family go bath in succession, using the same water, which becomes colder as time passes. Usually, the first person to use the bath is the privileged one in the family, either the father in normal circumstances, or the guest, if there is one, to show hospitality. That's why you're supposed to wash first before entering the bath: so you leave relatively clean water for the next person. The hot bath is for relaxing, not for washing.
Public baths are another story. That people would wash themselves before entering public bath is common sense. Only Japanese think it's common sense for private baths.
But Japanese people are incredibly proud of their culture. It's not surprising the author is gloating about "superior/common sense" Japanese culture