We sanitize, we don't sterilize. That means we don't kill everything, and there is still some bacteria in the wort/on the tools.
Your tap water has some bacteria in it too, and if you leave it out with some malt, some nasty things will eventually start growing.
BUT ...... the key is to pitch a healthy yeast with sufficient cells to overwhelm anything else in the wort. Once the yeast has got a grip on the wort and started to produce alcohol, it inhibits the growth of anything else (wild yeasts and actobacteria excluded).
Bacteria reproduce more rapidly than yeast, so you need to pitch a large amount of yeast by comparision to get a head start on any bacteria.
If you leave your wort a long time before pitching yeast or have poor pitching practice then you need to be really particular about sanitizing, possibly even boiling any top-up water from clean municipal sources.
If you pitch healthy yeast, and regularly get active fermentation within 24 hours, you don't have to be too concerned about using tap water.