"Fresh water ain't fresh." <- That's a good way of putting it ..... I'm going to need to try and remember it.
I'm right there with you on not drinking unboiled or untreated water .... though (if I'm recalling it correctly) from what I was taught even boiling & treating doesn't get rid of all the hazards -- just most/all (depending on what's present) of the living ones.
If I recall correctly one of the things we were taught in grade school was boiling and water treatments were good measures to use, but the safest treatment for surface water sources (if time and resources were available) was to distill the water by condensing water vapor on the underside of a pan/clean surface and funneling that into a canteen/reservoir for drinking. Which if memory serves was also taught with the fact that combustible containers (like paper cups, and birch bark pots) won't burn as long as they're in contact with water since the water takes the heat to boil and in doing so keeps the combustible material below its ignition point. The only (slight) disadvantage to distilled water is that it doesn't have some of the essential trace minerals that other water sources can provide. The other disadvantage was that distilling requires a fair amount of time and material (a container to boil water, a sanitary surface to collect and condense the water, a suitable container for collection, and all the fuel to boil the water).
Again going from memory: stagnant water was the most likely to support things growing in it, but even running water wasn't completely free of hazards as where it was running from, and what it might be eroding and carrying along could introduce it's own set of hazards. For example: mineral concentrations (even the safe ones can reach hazardous concentrations), runoff from areas with lots of fecal, or decaying matter present, along with all the obvious (and some not so obvious) human-caused hazards. (I'd rather not take this discussion into all the things that may not get tested for, monitored, or filtered out of public water sources, which may also find their way into surface water sources).
The other "good" sources of water were melted snow, and intentionally collected rainwater (assuming there isn't a whole lot of air pollutants in the area -- though frequent/hard precipitation can help reduce that, by knocking it down and putting the previously airborne material into surface water sources).
A few more useful links I just found:
WATER SAFETY FOR CAMPERS
A Guide to Drinking Water Treatment and Sanitation for Backcountry and Travel Use | Camping, Hiking, Travel | Drinking Water | Healthy Water | CDC
Ground Water — Safe Drinking Water Foundation (this one looks to have links to a fair amount of other educational material ... I think I may even have experienced some of the older versions of the EPA educational activities when I was in grade school a few decades ago)
Over all it's not something to be paranoid about, but it is something to be aware of so if/when the need arises you can make the water safe (enough) to drink. ...and of course this is one of those things where not knowing can indeed result in sickness or even death.
