Like many have mentioned before, aeration is no new concept... but utilizing smaller and smaller bubbles are for specific applications, such as detritus removal and maintenance assist in clearing up particulate matter in the water column.
The very nature of aeration just compounds the benefits of increasing oxygenation and degassing more efficiently than with the use of bigger bubbles. But once again not a new concept, just a new application of smaller and smaller bubbles.
I personally have been in the hobby since '95 and have utilized lots of "surge devices", aeration methods, etc. degassing and oxygenation assist in the chemical stability of the water chemistry in the aquarium be it saltwater or fresh.
The "claims" are not my own... they are OBSERVATIONS by many people employing the method from better growth (Possibly due to higher clarity and polishing of water utilizing floatation separation methodology for better light penetration) to pH stability (Possibly driving off excess metabolic gases such as CO2 when using fresh air)
The main ingredients to success of the micro-nanobubbling are these two characteristics:
***FRESH AIR*** and ***VERY VERY FINE BUBBLES***
:)