While in school I was taught and learned that all water went through a filtration system including sewage and after cleaning it would go back into the drinkable water lines running to our house.
I learned the same. I was quite disappointed later to find that, while all the sewage here goes through treatment, it does not get directly pumped back into the water pipes, but instead gets pumped back into the rivers. Although pragmatically speaking that makes more sense, since surface water is surface water, and completely separating these systems avoids any risk of contamination.