I live on the central Oregon coast, and a small town near me has had trouble with some kind of algae bloom in its reservoir for the last few summers. During those times, residents are advised to use bottled water, and are specifically told that boiling does not make the water safe to drink.
I have no idea what is in the water that boiling won’t fix, or even if the warning is valid, but that’s what the official announcements on the radio say.
At altitude the boiling point of water is lower so you may need to boil for longer at a lower temp to get the same effect. At 4000 meters the boiling point is only around 190 F.
I’m relieved to read on Wiki that cryptosporidium is most reliably killed by boiling, so there’s that, at least.
But methylmercury is produced by organisms. What about prions? I think they’re heat resistant.
Check the link above on the dangers of cyanobacteria; it’s the scientific term for blue-green algae.
Prions are resistant to heat. There are a handful of proteins that won’t denature with heat as well. Some toxins won’t degrade with reasonable heating either, such as urushiol, the wonderful chemical produced by poison ivy and its cousins, which survives even being put into a fire (every couple of years, someone burns poison ivy and either injures themselves or others from the vapor from the plants, frequently with fatal results).
That said, for most uses, boiling water SHOULD render it safe, save for those toxic blooms and chemical contamination. The vast majority of pathogens, if not killed outright, are dormant and would be unable to colonize your body.
Of course, the most reliable method, a method tens of thousands of years old, is to not drink the water at all, use it to make beer, the yeast would kill off the pathogens, rendering the beer safe to drink. 
What is the relevance of a lack of salt in the body to the OP?
Why would an unwashed berry, from the wild, make anybody sick?
I have eaten lots of wild berries over the decades and never got sick from a wild berry. Seems to me a wild berry is inherently clean.
I’m guessing he is referring to the ultimate in a “water-borne illness”, namely drinking too much water. I understand one of the most important effects of ODing on water itself is hyponatremia, i.e. ODing on water causes critically low sodium levels.
Maybe a bird shit on it, and rain washed enough off of it to make it hard to see.
1 in a million shot
Well, I was joking, because the usual place one encounters hyponatremia in the news is in stories of people who died after drinking too much water, usually while participating in marathons or the like. Pre-boiling the water obviously would not prevent the illness.
However, regarding “lack of salt” – note the last line in this passage from the Wikipedia article I cited: