This is my main objection to Tom Barr also. He makes a lot of conclusions based just on his own speculations. As far as I know, he never did any trully controlled experiment with well documented methodology. So no one can faithfully repeat his results. He uses a clay-based substrate in his main tank, very high CO2 levels, very low pH, very high light levels, quite high flow, big army of algae-eaters, do frequent water changes ... but in fact, we don't know all the parameters which may be in play in his tank. And this is the reason, why his method can't work universally and under all conditions (i.e. with different kinds of substrate, different water parameters, different plant species, different fish etc.). His method works in his tank under the given (fully unknown) conditions. But we don't know what these conditions really are. We know just what he lets us know or what he thinks is important for the
success. But that's not trully scientific method. That's nothing more than speculation based on some experience. Until he is able to controll all the variables in his tank, and tell us what variables are at play there and how they affect the whole, we won't be able to repeat the same results elsewhere in the world. We can be lucky and have the same or similar results, but we will never be sure why. It's never a good idea to do any experiments in fully uncontrolled environment like our tanks. And the main problem with T.Barr is that he did all his experiments right in his tank.
Takashi Amano is a similar example although he seems to know better what he's doing. His system is based on the use of concrete materials with concrete parameters. He doesn't let us know the exact methodology behind his system, but if you use his ADA system there's much higher chance you succeed as the crucial parts will be always the same (light intensity; nutrient content in the substrate and water column; filtration capacity, efficiency and flow; CO2 management). You are also recommended to use water with low hardness and alkalinity. If you follow his advice, you can repeat his success elsewhere in the world with much higher probability than with T.Barr's recommendations. Unfortunately, this know-how (hidden methodology) is very pricey. Even in this case we will never be sure why.