That reason is not really the point.
The point is that these plants, will suck up nutrients from the water column, in order to grow, one of those nutrients includes ammonia/nitrate. With access to CO2 in the atmosphere, which is much more concentrated than in aquarium water with no CO2 injection, they will grow much faster, which equals more nutrients being taken out of the water. This only really works if you have a light the plant can get to, with only ambient light, the plant won't grow as fast as it would if it had a light above it or direct sunlight.