First of all, many types of beer were historically not boiled. Quite a few still aren't. The mash, however, pasteurizes the beer.

That, however, doesn't last forever. In the conditions of the 18th century or whatever, microorganisms will get into the beer after mashing/boiling, so the heat treatment only helps for a while. The fermentation really does protect the beer afterwards, but it's a combination of low pH, alcohol, low oxygen, little nutrients, CO2, etc. Hops also help against gram-positive bacteria.