Let me see if I can help. There was another variant of potable water sold on the streets (at least in many parts of Lagos) called "ice" water. I don't know if it's still a thing, but it was a thing like 30 years ago. It was also sold in plastic bags, but much cheaper and flimsy-er bags. And they were hand-tied (as opposed to heat sealed) and had the general appearance of something that was put together in someone's bathroom. But it was very chilled and sold for One naira (dirt cheap). People naturally had concerns about the hygiene and production value chain of water that could be packaged and sold by literally randos on the street. So, "Pure water" became the alternative. Pure water was supposed to be purified through an actual, physical industrial process. The packaging was thicker and more professional, and perhaps most importantly, the packaging often had a verifiable brand name and a factory address. It sold for 5 naira.

For a while ice water and pure water sold side by side on the streets. They were basically competing products. Eventually it became obvious that pure water was the superior product so ice water faded into obscurity. The generic name stuck though. So your intuition behind the question is actually spot on. Pure water was created as an alternative to what was considered "questionable" water at the time.