As far as I'm aware, alcohol was used by humans for a long long time as a way to purify water drawn from unsafe sources

Unfortunately, OP, this is a long-standing misconception which it is my life's work to kill. While this previous answer from me is focused on Medieval Europe, the myth is founded there anyway, and there's no hydrological reason to think things were any different in the Muslim states. Groundwater is groundwater no matter where you go, mineral composition aside.

Adding to that, a user who no longer wishes to be tagged has a post re water sources in the MENA region.

Also, what Islam says and what Muslims do are two different things. Related, certainly, but different. After all, Christianity has an exact zero incidence of adultery, thievery, and similar such sins, no? If you'd like to learn more about drinking cultures in Muslim countries in the Middle Ages, I have a separate set of links for that.