The idea doesn't exist in Japan at least, one of the obvious reasons being that tea consumption grew greatly in popularity during the (Japanese) medieval era.

Tea was first introduced to Japan from China most probably in the 8th century. From that point, the popularity of tea drinking and tea cultivation spread first throughout the wealthy classes, and then later became a common drink for everyone in the early modern period.

Japanese tea is not necessarily made with boiling water, and so the sterilizing effect of heating the water is seperated from the image of the issue at hand. Pouring the water over the tea leaves also doesn't do much in the way of purifying bad water, and so it can be established that using bad water to make tea is a good way to get sick.

The widespread popularity of tea (and the fact that modern people are aware of that popularity) therefore prevents the belief that people couldn't drink water because it was dirty, for if the water were dirty people also wouldn't be drinking tea.

There are numerous other factors preventing such a myth from taking hold as well, for example that poor farmers were known as Mizu-nomi Byakusho, literally water drinking peasants, which identifies them as worse off than peasants who drank tea (or alcohol) with their meals.

A very basic knowledge of history would thus provide one with the ability to reject such a myth if it were to be brought up.

Edit: A few alterations to make it easier to understand