Rain water is going to contain various contaminants, in the form of gaseous aerial pollution that is absorbed by the water as it falls through the sky, and dispersed aerial salts that also get absorbed the same way. On top of this, every single water drop in a rain storm starts its journey as atmospheric moisture that first nucleates around something - and this is often aerial salts, but is frequently pollen, mushroom spores, larger bits of floating carbon, and so on. One can understand that rain waters from different regions of the world will contain different levels of "pollution" contamination, but rain that is closer to an ocean will also contain larger amounts of the ocean salts, as these also exists as free floating aerial salts as well.
As this water sits, it will naturally separate out a sediment. Even if you filter, unless you are using laboratory grade filters, the filters themselves can also impart microscopic particulates. Actually developing extremely fine filters that did not shed any matter whatsoever was quite a feat of technology in the past. Now I would say that just because we can trace where these contaminants may possibly come from does not mean that since there is a "chemical / material" explanation for it, that it's not meaningful observation worthy of further inquiry.
I've for a long time been involved in brewing alcohol and preparing agar samples- I only say this to mention that I know very well how to sterilize and clean. I've done tests with 7x distilled water, placed in a clean container (as clean as I can possibly make it), fully sealed, and after several months, it also created a particulate that, after settling on the bottom, while sitting in an undisturbed place, created a new form. That extremely fine particulate that settles at the bottom self-organized into a roughly cobweb / fractal / branched lightning shape, but even gently touching the outside of the jar was enough disturbance to break the structure - it dispersed like an extremely fine powder. I don't know what it was - I never repeated the experiment, but I have done other experiments with liquid which produced such a large amount of particulate that could swell up inside a liquid that it appears there is a sponge in there, but that spongy mass can also (with changing weather patterns or changing temperature or something else that I am not entirely sure what it is), shrink down to be little more than the thinnest amount of powder on the bottom, barely visible because of how little of it there is.
Certainly there is more going on and water can create some strange things. I would also suggest that rain water contains various amounts of types of bacteria - and incubating the rain water will also help to continually multiply the bacteria, which, on account of often having short lives / quicker doubling times, will also start to create a buildup of dead matter / organic debris in the water. Separating out this dried matter, if it is organic, can yield nitrogen compounds such as ammonia, for example if you tried to dry distill that powder.
