I'll give you the Reader's Digest message in that long video: Socks or filter floss serve a different mechanical function than a protein skimmer (yes, it is mechanical even though the process relies on charged bonds between interfaces), serves a different function than the chemical side, which can be accomplished via refugium (algae uptake) or media (GFO/Purigen/Activated carbon in particular). I'm leaving the biological side out, which is accomplished largely by your rock and sand. At the end of the day it is a matter of how do I feed corals and living organisms sufficiently while matching the rates which the system can adequately maintain required nutrient levels through consumption (by corals/algae/media) or minimization (mechanical removal).
In a small tank (I have a 14g one, which qualifies) large (or easy?) water changes certainly qualify for removal at both mechanical and chemical levels (diluting concentrations of NO3/PO4 while removing physical detritus blasted from sand/rock) as well as increasing concentrations of alk and calcium.
In that video they emphasize that yes, you can over-remove if it is to the detriment of the organisms needing said "nutrients" to flourish. Conversely (as is the case with my tank) I have skimmer and mechanical means and large (80%) water changes and yet this isn't sufficient to keep long hair algae at bay. The analysis is a bit more complex than how large or small a tank is, and large or more frequent water changes (enabled by smaller tanks) is just a piece of the puzzle.
The ideal goal is to be able to put a lot of food input into the tank for coral growth and at the same time export a lot of the unused nutrients. Lot in/lot out, versus minimal in, minimal left behind, which can result in pale corals, stunted growth, less than healthy livestock. This rate of input/output is very much dependent on the stage of lifecycle of the tank. A new tank is going to consume very little, while a 5 year old tank covered inch by inch with corals is going to need a much larger input (and will also consume a much larger input meaning less NO3/PO4 left behind).
To me, the trick in an anemone specific tank is that you need to wait for awhile to achieve the stability needed by 'nems, which means there is much more likely chance of a nutrient increase and algae takeover, especially in a dry rock based system.
If anyone has ideas how to bridge the gap between a new sterile system and an anemone dominated tank, I'm all ears.
@OrionN?
