Drinking straight out of the stream is more dramatic and gives more of a "wild man" impression.

Notice that he boiled the water and pointed out his likely mistake after he got sick.

He might've been taking the coyote teacher approach, knowing that people would learn more from watching his mistake than a lecture on purifying water.

As a side observation, notice how he takes the metal cup right off the fire in every episode and puts it right to his lips? Don't try this at home kids!