If the stream is within a shouting distance of the camp, what is the point of the roll? This isn't a challenging action. My interpretation is that the character looks within the whole hex for a source of clean water.
1) it was an example. Substitute with a thrilling short story, where the forager returns to the camp and tells everybody about their discovery, and every one grabs their waterskins and follow if you would prefer.
2) Being within shouting distance of the camp does not mean it is obvious. PCs arent omniscient, and they don't automatically know what is under every rock and behind every bush within 300 meters of their camp. Escpecially not in a forest, for example, where sight might be very limited. Even on an open field it might be obscured by tall grass, a gentle slope, or just very tiny. A stream with servicable drinking water does not need to be large. And streams can run under ground for long streches, only to trickle out in a small spott in a hillside before being swallowed by the ground again.
Searching the entire hex does is not the same thing as the source being located at the furthest possible distance. The time spent might as well be explained by the water trickling out very slowly, so it takes those six hours for everyone to actually fill their waterskins.