"is it correct to assume?"
No. It seems like we keep going over the same subject, over and over.
First of all, you have to assess the water quality to decide what the likely risks are. Since we aren't carrying instruments, about all we can rely on are the clarity of the water and it's distance from mammal habitations.
There are a few different water risks, so you have to guess what you are up against. A virus can cause disease, and some are pretty nasty, like hepatitis. A poor filter won't touch that. Bacteria can cause disease, and some are pretty nasty, especially some of the tropical types. A poor filter won't touch that. Protozoans can be in the form of microscopic eggs, called cysts. They are not normally lethal, and it may take some number of them to actually make you sick. Or not. A poor filter may not be very successful against them. Then you have chemical contaminants, like agricultural and industrial chemicals. You almost have to go after those with chemical treatment.
There are multiple risks, and there are multiple methods of prevention. You can boil the water. You can filter it. You can treat it chemically. You can treat it with strong UV light. There may be other methods. However, if you don't know what you are up against, you have to make a stab at it. In some of the risks, if you can eliminate 99% of the organisms, then that is probably good enough. There are some rare risks that would almost require you to eliminate 100% of it to feel safe, but those are rare.
With all that in mind, what do I do? I travel mostly high in the Sierra Nevada range, and the snow melt is cold even into the summer. Normally, I carry a tiny 2-micron filter hooked up for gravity flow, and some household bleach. I filter the raw water and then drink it. If I think the raw water looks suspicious, then I pre-treat it with the bleach. If either of those methods is gone, then I boil the water. So, somehow the water gets treated one way or the other, and I have never gotten sick from the water for the decades that I have lived in California. Note that the next person might be more or less sensitive, so they need to adjust their methods.
Yes, it is possible to get sick from a few drops of raw water left on screw threads of a water bottle. Is it likely? Hard to tell. Do you feel lucky?