I agree that filters are not necessary, they are mainly just for removing solids to make the water look clearer but on larger tanks I feel that have the added use of keeping an even temperature.
As for stagnant water ... what do you mean? The 'puddles' these fish may be found in are much larger than 20g, and most certainly do not sit for a year without fresh water. Usually they are small to large ponds left after flooding rivers, but they flood with the rains and do not remain as ponds. In the Amazon the rivers flood from November through June which is a significant portion of the year.
As for parameters, do you test for fish pee? Pheromones? etc etc. That was my point, there is far more waste produced than Ammonia (which goes to nitrite, then nitrate, then nitrogen). We can't test for them without expensive instrumentation, so who knows what levels they get to, and at what point they become a problem. I doubt anyone has even studied it.
Please don't think I have anything against using soil, or that it doesn't work, I just don't believe it is truly in the best interest of the fish to forego water changes.
EDIT: And ninja'd by Byron, haha, I take too long typing out my responses...