Ok. So I am just speculating here. You can read if you have nothing better to do but these are just my current thoughts.
I think that in a CO2 injected or liquid carbon tanks with heavy fertilization, the plants themselves p roduce mass amount of organics when growing fast, which also happens to coat the leaves themselves thus if not enough cleaning//siphoning/water changes are done, one ends up with algae outbreaks in those tanks as the build up is more than the tank can handle via microorganism activity and algae just jumps in to help out in the presence of light, same as in natural systems when there's too much of a something.
The substrate in El Natural tanks would have a way bigger organic load processing capability and microorganism diversity I'd imagine than some normal inert substrate planted tanks with a pile of wood on one side loaded with anubias, java fern and java moss and a few stems sticking out behind it, barely much plants planted in the substrate itself bar some short rooters, regular siphoning, heavy wiping/cleaning, etc.. In most inert substrate tanks nitrification happens only in the surface layer of the substrate where there's oxygen.
In El natural we are advised to plant heavy, lots of fast growing plants and also heavy rooters. This results in great oxygen production for any tank, but in El natural, most importantly, oxygen is driven deep in the soil substrate itself via big plant roots which in turn supports heavy decomposition of organics as well as nitrification and other processes to a greater extent, and then plants in turn use the products of those processes maybe preventing much organics from escaping the soil and building up in the water column which could trigger multiplication of organic lovers such as algae spores waiting in the light for their share of left overs.
So a well designed soil tank is sort of a super biofilter one can't buy in the shop.
To summarise I think organics do play a role in algae I'd imagine , if algae has organics and light at the same time. The solution is either to reduce/remove organics via heavy cleaning/water changes and inject CO2 and ferts via the water column for the plants or create conditions in the tank so the tank can do that for you instead to a great extent. Promote high oxygen production in the soil and water column and media for organics decomposition and microorganism activity which lacks light in order not to attract algae instead and you are a happy lazy bunny. Deprive the tank from that and you've got to be on top of it because it can't do nothing for itself alone.
I mean it's not that hard to notice the difference in functionality between a El Natural and a High Tech.
Try not to water change or siphon a well functioning El Natural tank for 6 months, nothing much will happen as long as you trim back the plants so the tank doesn't turn into a spaghetti dinner. Try to do the same in a high tech tank for 1 month and you'll be loaded with algae.
Maybe high tech enthusiast are praising ADA Amazonia and similar substrates because they do provide similar functionality to a natural soil substrate used in El Natural tanks and are just capable of processing heavy organics, leading to more stable tanks that allow for some user mistakes, overstocking, or even a week holiday from time to time

At the same time even an inert gravel substrate in time becomes highly functional if planted, stabilizing a previously algae infested tanks that were incapable of processing much organics.
But a proper soil just gives you that effect way faster.